Journal of the London Mathematical Society-Second Series最新文献_第3页

Cartan projections of fiber products and non-quasi-isometric embeddings 纤维积的卡坦投影和非等轴等距嵌入

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-15 DOI: 10.1112/jlms.70004

Konstantinos Tsouvalas

{"title":"Cartan projections of fiber products and non-quasi-isometric embeddings","authors":"Konstantinos Tsouvalas","doi":"10.1112/jlms.70004","DOIUrl":"https://doi.org/10.1112/jlms.70004","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> be a finitely generated group and <math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> be a normal subgroup of <math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math>. The fiber product of <math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math> with respect to <math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> is the subgroup <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 <msub>\u0000 <mo>×</mo>\u0000 <mi>N</mi>\u0000 </msub>\u0000 <mi>Γ</mi>\u0000 <mo>=</mo>\u0000 <mo>{</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>γ</mi>\u0000 <mo>,</mo>\u0000 <mi>γ</mi>\u0000 <mi>w</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>:</mo>\u0000 <mi>γ</mi>\u0000 <mo>∈</mo>\u0000 <mi>Γ</mi>\u0000 <mo>,</mo>\u0000 <mi>w</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$Gamma times _N Gamma =big lbrace (gamma, gamma w): gamma in Gamma, w in Nbig rbrace$</annotation>\u0000 </semantics></math> of the direct product <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 <mo>×</mo>\u0000 <mi>Γ</mi>\u0000 </mrow>\u0000 <annotation>$Gamma times Gamma$</annotation>\u0000 </semantics></math>. For every representation <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 <mo>:</mo>\u0000 <mi>Γ</mi>\u0000 <msub>\u0000 <mo>×</mo>\u0000 <mi>N</mi>\u0000 </msub>\u0000 <mi>Γ</mi>\u0000 <mo>→</mo>\u0000 <msub>\u0000 <mi>GL</mi>\u0000 <mi>d</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$rho:Gamma times _N Gamma rightarrow mathsf {GL}_d(k)$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotatio","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142439107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sharp propagation of chaos for the ensemble Langevin sampler 集合朗之文采样器的混沌急剧传播

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-14 DOI: 10.1112/jlms.13008

U. Vaes

{"title":"Sharp propagation of chaos for the ensemble Langevin sampler","authors":"U. Vaes","doi":"10.1112/jlms.13008","DOIUrl":"https://doi.org/10.1112/jlms.13008","url":null,"abstract":"The aim of this paper is to revisit propagation of chaos for a Langevin-type interacting particle system recently proposed as a method to sample probability measures. The interacting particle system we consider coincides, in the setting of a log-quadratic target distribution, with the ensemble Kalman sampler [SIAM J. Appl. Dyn. Syst. 19 (2020), no. 1, 412–441], for which propagation of chaos was first proved by Ding and Li in [SIAM J. Math. Anal. 53 (2021), no. 2, 1546–1578]. Like these authors, we prove propagation of chaos with an approach based on a synchronous coupling, as in Sznitman's classical argument. Instead of relying on a boostrapping argument, however, we use a technique based on stopping times in order to handle the presence of the empirical covariance in the coefficients of the dynamics. The use of stopping times to handle the lack of global Lipschitz continuity in the coefficients of stochastic dynamics originates from numerical analysis [SIAM J. Numer. Anal. 40 (2002), no. 3, 1041–1063] and was recently employed to prove mean-field limits for consensus-based optimization and related interacting particle systems [arXiv:2312.07373, 2023; Math. Models Methods Appl. Sci. 33 (2023), no. 2, 289–339]. In the context of ensemble Langevin sampling, this technique enables proving pathwise propagation of chaos with optimal rate, whereas previous results were optimal only up to a positive <math>\u0000 <semantics>\u0000 <mi>ε</mi>\u0000 <annotation>$varepsilon$</annotation>\u0000 </semantics></math>.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142435326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tubings, chord diagrams, and Dyson–Schwinger equations 管线、弦图和戴森-施文格方程

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-13 DOI: 10.1112/jlms.70006

Paul-Hermann Balduf, Amelia Cantwell, Kurusch Ebrahimi-Fard, Lukas Nabergall, Nicholas Olson-Harris, Karen Yeats

引用次数: 0

Heavenly metrics, hyper-Lagrangians and Joyce structures 天堂度量、超拉格朗日和乔伊斯结构

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-11 DOI: 10.1112/jlms.13009

Maciej Dunajski, Timothy Moy

{"title":"Heavenly metrics, hyper-Lagrangians and Joyce structures","authors":"Maciej Dunajski, Timothy Moy","doi":"10.1112/jlms.13009","DOIUrl":"https://doi.org/10.1112/jlms.13009","url":null,"abstract":"In [Proc. Sympos. Pure Math., American Mathematical Society, Providence, RI, 2021, pp. 1–66], Bridgeland defined a geometric structure, named a Joyce structure, conjectured to exist on the space <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> of stability conditions of a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msub>\u0000 <mi>Y</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$CY_3$</annotation>\u0000 </semantics></math> triangulated category. Given a non-degeneracy assumption, a feature of this structure is a complex hyper-Kähler metric with homothetic symmetry on the total space <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <mi>T</mi>\u0000 <mi>M</mi>\u0000 </mrow>\u0000 <annotation>$X = TM$</annotation>\u0000 </semantics></math> of the holomorphic tangent bundle. Generalising the isomonodromy calculation which leads to the <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$A_2$</annotation>\u0000 </semantics></math> Joyce structure in [Math. Ann. 385 (2023), 193–258], we obtain an explicit expression for a hyper-Kähler metric with homothetic symmetry via construction of the isomonodromic flows of a Schrödinger equation with deformed polynomial oscillator potential of odd-degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$2n+1$</annotation>\u0000 </semantics></math>. The metric is defined on a total space <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> of complex dimension <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$4n$</annotation>\u0000 </semantics></math> and fibres over a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$2n$</annotation>\u0000 </semantics></math>-dimensional manifold <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.13009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

First-order asymptotic perturbation theory for extensions of symmetric operators 对称算子扩展的一阶渐近扰动理论

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-11 DOI: 10.1112/jlms.13005

Yuri Latushkin, Selim Sukhtaiev

{"title":"First-order asymptotic perturbation theory for extensions of symmetric operators","authors":"Yuri Latushkin, Selim Sukhtaiev","doi":"10.1112/jlms.13005","DOIUrl":"https://doi.org/10.1112/jlms.13005","url":null,"abstract":"This work offers a new prospective on asymptotic perturbation theory for varying self-adjoint extensions of symmetric operators. Employing symplectic formulation of self-adjointness, we use a version of resolvent difference identity for two arbitrary self-adjoint extensions that facilitates asymptotic analysis of resolvent operators via first-order expansion for the family of Lagrangian planes associated with perturbed operators. Specifically, we derive a Riccati-type differential equation and the first-order asymptotic expansion for resolvents of self-adjoint extensions determined by smooth one-parameter families of Lagrangian planes. This asymptotic perturbation theory yields a symplectic version of the abstract Kato selection theorem and Hadamard–Rellich-type variational formula for slopes of multiple eigenvalue curves bifurcating from an eigenvalue of the unperturbed operator. The latter, in turn, gives a general infinitesimal version of the celebrated formula equating the spectral flow of a path of self-adjoint extensions and the Maslov index of the corresponding path of Lagrangian planes. Applications are given to quantum graphs, periodic Kronig–Penney model, elliptic second-order partial differential operators with Robin boundary conditions, and physically relevant heat equations with thermal conductivity.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Codimension two mean curvature flow of entire graphs 整图的二维平均曲率流

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-10 DOI: 10.1112/jlms.13000

Andreas Savas Halilaj, Knut Smoczyk

{"title":"Codimension two mean curvature flow of entire graphs","authors":"Andreas Savas Halilaj, Knut Smoczyk","doi":"10.1112/jlms.13000","DOIUrl":"https://doi.org/10.1112/jlms.13000","url":null,"abstract":"We consider the graphical mean curvature flow of maps <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbf {f}:{mathbb {R}^{m}}rightarrow {mathbb {R}^{n}}$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$mgeqslant 2$</annotation>\u0000 </semantics></math>, and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well-known maximum principle of Ecker and Huisken derived in their seminal paper [Ann. of Math. (2) 130:3(1989), 453–471]. In the case of uniformly area decreasing maps <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbf {f}:{mathbb {R}^{m}} rightarrow {mathbb {R}^{2}}$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$mgeqslant 2$</annotation>\u0000 </semantics></math>, we use this maximum principle to show that the graphicality and the area decreasing property are preserved. Moreover, if the initial graph is asymptotically conical at infinity, we prove that the normalized mean curvature flow smoothly converges to a self-expander.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.13000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Colouring versus density in integers and Hales–Jewett cubes 整数和黑尔斯-祖耶特立方体中的着色与密度关系

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-10 DOI: 10.1112/jlms.12987

Christian Reiher, Vojtěch Rödl, Marcelo Sales

{"title":"Colouring versus density in integers and Hales–Jewett cubes","authors":"Christian Reiher, Vojtěch Rödl, Marcelo Sales","doi":"10.1112/jlms.12987","DOIUrl":"https://doi.org/10.1112/jlms.12987","url":null,"abstract":"We construct for every integer <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$kgeqslant 3$</annotation>\u0000 </semantics></math> and every real <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mi>k</mi>\u0000 </mfrac>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mu in (0, frac{k-1}{k})$</annotation>\u0000 </semantics></math> a set of integers <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <mi>X</mi>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>μ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$X=X(k, mu)$</annotation>\u0000 </semantics></math> which, when coloured with finitely many colours, contains a monochromatic <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-term arithmetic progression, whilst every finite <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Y</mi>\u0000 <mo>⊆</mo>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <annotation>$Ysubseteq X$</annotation>\u0000 </semantics></math> has a subset <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 <mo>⊆</mo>\u0000 <mi>Y</mi>\u0000 </mrow>\u0000 <annotation>$Zsubseteq Y$</annotation>\u0000 </semantics></math> of size <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>Z</mi>\u0000 <mo>|</mo>\u0000 <mo>⩾</mo>\u0000 <mi>μ</mi>\u0000 <mo>|</mo>\u0000 <mi>Y</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <annotation>$|Z|geqslant mu |Y|$</annotation>\u0000 </semantics></math> that is free of arithmetic progressions of length <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>. T","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12987","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Least energy solutions for a class of ( p 1 , p 2 ) $(p_{1}, p_{2})$ -Kirchhoff-type problems in R N $mathbb {R}^{N}$ with general nonlinearities 具有一般非线性的 R N $mathbb {R}^{N}$ 中一类 ( p 1 , p 2 ) $(p_{1}, p_{2})$ -Kirchhoff-type 问题的最小能量解法

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-07 DOI: 10.1112/jlms.13004

Vincenzo Ambrosio

{"title":"Least energy solutions for a class of \u0000 \u0000 \u0000 (\u0000 \u0000 p\u0000 1\u0000 \u0000 ,\u0000 \u0000 p\u0000 2\u0000 \u0000 )\u0000 \u0000 $(p_{1}, p_{2})$\u0000 -Kirchhoff-type problems in \u0000 \u0000 \u0000 R\u0000 N\u0000 \u0000 $mathbb {R}^{N}$\u0000 with general nonlinearities","authors":"Vincenzo Ambrosio","doi":"10.1112/jlms.13004","DOIUrl":"https://doi.org/10.1112/jlms.13004","url":null,"abstract":"We examine the following <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p_{1}, p_{2})$</annotation>\u0000 </semantics></math>-Kirchhoff-type problem:\u0000\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.13004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The excedance quotient of the Bruhat order, quasisymmetric varieties, and Temperley–Lieb algebras 布鲁哈特阶的赋形商、准对称品种和滕伯里-里布代数

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-07 DOI: 10.1112/jlms.13007

Nantel Bergeron, Lucas Gagnon

{"title":"The excedance quotient of the Bruhat order, quasisymmetric varieties, and Temperley–Lieb algebras","authors":"Nantel Bergeron, Lucas Gagnon","doi":"10.1112/jlms.13007","DOIUrl":"https://doi.org/10.1112/jlms.13007","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mi>Q</mi>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mtext>…</mtext>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$R_n=mathbb {Q}[x_1,x_2,ldots ,x_n]$</annotation>\u0000 </semantics></math> be the ring of polynomials in <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> variables and consider the ideal <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>⟨</mo>\u0000 <msubsup>\u0000 <mi>QSym</mi>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 </msubsup>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <mo>⊆</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$langle mathrm{QSym}_{n}^{+}rangle subseteq R_n$</annotation>\u0000 </semantics></math> generated by quasisymmetric polynomials without constant term. It was shown by J. C. Aval, F. Bergeron, and N. Bergeron that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>dim</mo>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mrow>\u0000 <mo>⟨</mo>\u0000 <msubsup>\u0000 <mi>QSym</mi>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 </msubsup>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.13007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform 具有可逆射线变换的流形上大固定频率的各向异性卡尔德龙问题

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-05 DOI: 10.1112/jlms.13006

Shiqi Ma, Suman Kumar Sahoo, Mikko Salo

引用次数: 0