Pure and Applied Mathematics Quarterly最新文献_第3页

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-05-15 DOI: 10.4310/pamq.2024.v20.n3.a7

A. Garsia, G. Ganzberger

{"title":"Fibonacci polynomials","authors":"A. Garsia, G. Ganzberger","doi":"10.4310/pamq.2024.v20.n3.a7","DOIUrl":"https://doi.org/10.4310/pamq.2024.v20.n3.a7","url":null,"abstract":"The Fibonacci polynomials ${lbrace F_n (x) rbrace}_{n geq 0}$ have been studied in multiple ways, [$href{https://www.imsc.res.in/~viennot/wa_files/viennotop1983-ocr.pdf}{1}$,$href{https://www.fq.math.ca/Scanned/11-3/hoggatt1.pdf}{6}$,$href{https://www.fq.math.ca/Scanned/12-2/hoggatt1.pdf}{7}$,$href{https://www.rivmat.unipr.it/fulltext/1995-4/1995-4-15.pdf}{9}$].In this paper we study them by means of the theory of heaps of Viennot [11, 12]. In this setting our polynomials form a basis ${lbrace P_n (x) rbrace}_{n geq 0}$ with $P_n (x)$ monic of degree $n$. This given, we are forced to set $P_n (x) = F_{n+1} (x)$. The heaps setting extends the Flajolet view$href{https://doi.org/10.1016/0012-365X(80)90050-3}{[4]}$ of the classical theory of orthogonal polynomials given by a three term recursion [3, 10]. Thus with heaps most of the identities for the polynomials $P_n (x)$’s can be derived by combinatorial arguments. Using the present setting we derive a variety of new identities. We must mention that the theory of heaps is presented here without restrictions. This is much more than needed to deal with the Fibonacci polynomials. We do this to convey a flavor of the power of heaps. In $href{https://link.springer.com/book/10.1007/978-3-030-58373-6 }{[5]}$ there is a chapter dedicated to heaps where most of its contents are dedicated to applications of the theory. In this paper we improve upon the developments in $href{https://link.springer.com/book/10.1007/978-3-030-58373-6 }{[5]}$ by adding details that were omitted there.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Asymptotic properties of tensor powers in symmetric tensor categories 对称张量类别中张量幂的渐近特性

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-05-15 DOI: 10.4310/pamq.2024.v20.n3.a4

Kevin Coulembier, Pavel Etingof, Victor Ostrik

{"title":"Asymptotic properties of tensor powers in symmetric tensor categories","authors":"Kevin Coulembier, Pavel Etingof, Victor Ostrik","doi":"10.4310/pamq.2024.v20.n3.a4","DOIUrl":"https://doi.org/10.4310/pamq.2024.v20.n3.a4","url":null,"abstract":"Let $G$ be a group and $V$ a finite dimensional representation of $G$ over an algebraically closed field $k$ of characteristic $p gt 0$. Let $d_n (V)$ be the number of indecomposable summands of $V^{oplus n}$ of nonzero dimension $mod p$. It is easy to see that there exists a limit $delta (V) := lim_{n to infty} d_n(V)^{1/n}$, which is positive (and $geq 1$) $operatorname{iff}$ $V$ has an indecomposable summand of nonzero dimension $mod p$. We show that in this case the number[c(V ) := underset{n to infty}{lim inf} frac{d_n(V)}{delta(V)^n}$ in [0, 1]]is strictly positive and[log(c(V)^{-1}) = O(delta(V)^2),]and moreover this holds for any symmetric tensor category over $k$of moderate growth. Furthermore, we conjecture that in fact[log(c(V)^{-1}) = O(delta(V))](which would be sharp), and prove this for $p = 2, 3$; in particular, for $p = 2$ we show that $c(V) geq 3^{frac{4}{3} delta (V)+1}$. The proofs are based on the characteristic $p$ version of Deligne’s theorem for symmetric tensor categories obtained in $href{ https://dx.doi.org/10.4007/annals.2023.197.3.5}{[textrm{CEO}}]$. We also conjecture a classification of semisimple symmetric tensor categories of moderate growth which is interesting in its own right and implies the above conjecture for all $p$, and illustrate this conjecture by describing the semisimplification of the modular representation category of a cyclic $p$-group. Finally, we study the asymptotic behavior of the decomposition of $V^{oplus n}$ in characteristic zero using Deligne’s theorem and the Macdonald–Mehta–Opdam identity.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"208 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Adler–Oevel-Ragnisco type operators and Poisson vertex algebras 阿德勒-奥维尔-拉格尼斯科型算子和泊松顶点代数

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-05-15 DOI: 10.4310/pamq.2024.v20.n3.a5

Alberto De Sole, Victor G. Kac, Daniele Valeri

引用次数: 0

The semi-infinite cohomology of Weyl modules with two singular points 具有两个奇异点的 Weyl 模块的半无限同调

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-05-15 DOI: 10.4310/pamq.2024.v20.n3.a6

Giorgia Fortuna, Davide Lombardo, Andrea Maffei, Valerio Melani

引用次数: 0

Analytic and Reidemeister torsions of digraphs and path complexes 数图和路径复合体的解析和雷德梅斯特扭转

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-04-03 DOI: 10.4310/pamq.2024.v20.n2.a3

Alexander Grigor’yan, Yong Lin, Shing-Tung Yau

引用次数: 0

Mirror symmetry for open $r$-spin invariants 开放式 $r$ 自旋不变式的镜像对称性

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-04-03 DOI: 10.4310/pamq.2024.v20.n2.a9

Mark Gross, Tyler L. Kelly, Ran J. Tessler

引用次数: 0

Twisting pure spinor superfields, with applications to supergravity 扭曲纯自旋超场，以及在超引力中的应用

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-04-03 DOI: 10.4310/pamq.2024.v20.n2.a2

Ingmar Saberi, Brian R. Williams

{"title":"Twisting pure spinor superfields, with applications to supergravity","authors":"Ingmar Saberi, Brian R. Williams","doi":"10.4310/pamq.2024.v20.n2.a2","DOIUrl":"https://doi.org/10.4310/pamq.2024.v20.n2.a2","url":null,"abstract":"We study a functor from two-step nilpotent super Lie algebras to sheaves of commutative differential graded algebras on the site of smooth $d$-manifolds, where $d$ is the dimension of the even subalgebra. The functor generalizes the pure spinor superfield formalism as studied in the physics literature. We prove that the functor commutes with deformations of the super Lie algebra by a Maurer–Cartan element, and apply the result to compute twists of various free supergravity theories and supersymmetric field theories of physical interest. Our results show that, just as the component fields of supersymmetric multiplets are the vector bundles associated to the equivariant Koszul homology of the variety of square-zero elements in the supersymmetry algebra, the component fields of the holomorphic twists of the corresponding multiplets are the holomorphic vector bundles associated to the equivariant Koszul homology of square-zero elements in the twisted supersymmetry algebra. The BRST or BV differentials of the free multiplet are induced by the brackets of the corresponding super Lie algebra in each case. We make this precise in a variety of examples; applications include rigorous computations of the minimal twists of eleven-dimensional and type IIB supergravity, in the free perturbative limit. The latter result proves a conjecture by Costello and Li, relating the IIB multiplet directly to a presymplectic BV version of minimal BCOV theory.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"188 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Stability of Minkowski spacetime in exterior regions 外部区域闵科夫斯基时空的稳定性

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-04-03 DOI: 10.4310/pamq.2024.v20.n2.a4

Dawei Shen

引用次数: 0

Monotone quantities of $p$-harmonic functions and their applications p$谐函数的单调量及其应用

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-04-03 DOI: 10.4310/pamq.2024.v20.n2.a1

Sven Hirsch, Pengzi Miao, Luen-Fai Tam

引用次数: 0

Deformations of Fano manifolds with weighted solitons 法诺流形的变形与加权孤子