发布求助
文献互助 智能选刊 最新文献

Discrete Analysis最新文献

筛选
英文 中文
Stronger arithmetic equivalence 更强的算术等价
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2021-04-05 DOI: 10.19086/da.29452
Andrew Sutherland
{"title":"Stronger arithmetic equivalence","authors":"Andrew Sutherland","doi":"10.19086/da.29452","DOIUrl":"https://doi.org/10.19086/da.29452","url":null,"abstract":"Motivated by a recent result of Prasad, we consider three stronger notions of arithmetic equivalence: local integral equivalence, integral equivalence, and solvable equivalence. In addition to having the same Dedekind zeta function (the usual notion of arithmetic equivalence), number fields that are equivalent in any of these stronger senses must have the same class number, and solvable equivalence forces an isomorphism of adele rings. Until recently the only nontrivial example of integral and solvable equivalence arose from a group-theoretic construction of Scott that was exploited by Prasad. Here we provide infinitely many distinct examples of solvable equivalence, including a family that contains Scott's construction as well as an explicit example of degree 96. We also construct examples that address questions of Scott, and of Guralnick and Weiss, and shed some light on a question of Prasad.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45240803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Random volumes in d-dimensional polytopes d维多面体中的随机体积
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2020-02-26 DOI: 10.19086/DA.17109
A. Frieze, W. Pegden, T. Tkocz
{"title":"Random volumes in d-dimensional polytopes","authors":"A. Frieze, W. Pegden, T. Tkocz","doi":"10.19086/DA.17109","DOIUrl":"https://doi.org/10.19086/DA.17109","url":null,"abstract":"Suppose we choose $N$ points uniformly randomly from a convex body in $d$ dimensions. How large must $N$ be, asymptotically with respect to $d$, so that the convex hull of the points is nearly as large as the convex body itself? It was shown by Dyer-Furedi-McDiarmid that exponentially many samples suffice when the convex body is the hypercube, and by Pivovarov that the Euclidean ball demands roughly $d^{d/2}$ samples. We show that when the convex body is the simplex, exponentially many samples suffice; this then implies the same result for any convex simplicial polytope with at most exponentially many faces.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43115935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 9
Joints formed by lines and a $k$-plane, and a discrete estimate of Kakeya type 由直线和k平面组成的关节，以及Kakeya型的离散估计
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2019-11-20 DOI: 10.19086/DA.18361
A. Carbery, Marina Iliopoulou
{"title":"Joints formed by lines and a $k$-plane, and a discrete estimate of Kakeya type","authors":"A. Carbery, Marina Iliopoulou","doi":"10.19086/DA.18361","DOIUrl":"https://doi.org/10.19086/DA.18361","url":null,"abstract":"Let $mathcal{L}$ be a family of lines and let $mathcal{P}$ be a family of $k$-planes in $mathbb{F}^n$ where $mathbb{F}$ is a field. In our first result we show that the number of joints formed by a $k$-plane in $mathcal{P}$ together with $(n-k)$ lines in $mathcal{L}$ is $O_n(|mathcal{L}||mathcal{P}|^{1/(n-k)}$). This is the first sharp result for joints involving higher-dimensional affine subspaces, and it holds in the setting of arbitrary fields $mathbb{F}$. In contrast, for our second result, we work in the three-dimensional Euclidean space $mathbb{R}^3$, and we establish the Kakeya-type estimate begin{equation*}sum_{x in J} left(sum_{ell in mathcal{L}} chi_ell(x)right)^{3/2} lesssim |mathcal{L}|^{3/2}end{equation*} where $J$ is the set of joints formed by $mathcal{L}$; such an estimate fails in the setting of arbitrary fields. This result strengthens the known estimates for joints, including those counting multiplicities. Additionally, our techniques yield significant structural information on quasi-extremisers for this inequality.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43994732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
An efficient container lemma 一个有效容器引理
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2019-10-21 DOI: 10.19086/DA.17354
J. Balogh, W. Samotij
{"title":"An efficient container lemma","authors":"J. Balogh, W. Samotij","doi":"10.19086/DA.17354","DOIUrl":"https://doi.org/10.19086/DA.17354","url":null,"abstract":"We prove a new, efficient version of the hypergraph container theorems that is suited for hypergraphs with large uniformities. The main novelty is a refined approach to constructing containers that employs simple ideas from high-dimensional convex geometry. The existence of smaller families of containers for independent sets in such hypergraphs, which is guaranteed by the new theorem, allows us to improve upon the best currently known bounds for several problems in extremal graph theory, discrete geometry, and Ramsey theory.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41742931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 11
A characterization of polynomials whose high powers have non-negative coefficients 具有非负系数的高幂多项式的一个性质
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2019-10-15 DOI: 10.19086/DA.18560
Marcus Michelen, J. Sahasrabudhe
{"title":"A characterization of polynomials whose high powers have non-negative coefficients","authors":"Marcus Michelen, J. Sahasrabudhe","doi":"10.19086/DA.18560","DOIUrl":"https://doi.org/10.19086/DA.18560","url":null,"abstract":"Let $f in mathbb{R}[x]$ be a polynomial with real coefficients. We say that $f$ is eventually non-negative if $f^m$ has non-negative coefficients for all sufficiently large $m in mathbb{N}$. In this short note, we give a classification of all eventually non-negative polynomials. This generalizes a theorem of De Angelis, and proves a conjecture of Bergweiler, Eremenko and Sokal","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48029879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3
The structure of multiplicative functions with small partial sums 具有小部分和的乘法函数的结构
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2019-09-28 DOI: 10.19086/da.11963
Dimitris Koukoulopoulos, K. Soundararajan
{"title":"The structure of multiplicative functions with small partial sums","authors":"Dimitris Koukoulopoulos, K. Soundararajan","doi":"10.19086/da.11963","DOIUrl":"https://doi.org/10.19086/da.11963","url":null,"abstract":"The Landau-Selberg-Delange method provides an asymptotic formula for the partial sums of a multiplicative function whose average value on primes is a fixed complex number $v$. The shape of this asymptotic implies that $f$ can get very small on average only if $v=0,-1,-2,dots$. Moreover, if $v<0$, then the Dirichlet series associated to $f$ must have a zero of multiplicity $-v$ at $s=1$. In this paper, we prove a converse result that shows that if $f$ is a multiplicative function that is bounded by a suitable divisor function, and $f$ has very small partial sums, then there must be finitely many real numbers $gamma_1$, $dots$, $gamma_m$ such that $f(p)approx -p^{igamma_1}-cdots-p^{-igamma_m}$ on average. The numbers $gamma_j$ correspond to ordinates of zeroes of the Dirichlet series associated to $f$, counted with multiplicity. This generalizes a result of the first author, who handled the case when $|f|le 1$ in previous work.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47888538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3
Decomposition of random walk measures on the one-dimensional torus. 一维环面上随机游动测度的分解。
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2019-09-15 DOI: 10.19086/da.11888
T. Gilat
{"title":"Decomposition of random walk measures on the one-dimensional torus.","authors":"T. Gilat","doi":"10.19086/da.11888","DOIUrl":"https://doi.org/10.19086/da.11888","url":null,"abstract":"The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a sufficiently large subset $S$ of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures. The first one $mu_1$ has the property that the random walk with initial distribution $mu_1$ evolved by the action of $S$ equidistributes very fast. The second measure $mu_2$ in the decomposition is concentrated on very small neighborhoods of a small number of points.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41901623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An algebraic inverse theorem for the quadratic Littlewood-Offord problem, and an application to Ramsey graphs 二次Littlewood-Offord问题的代数逆定理及其在Ramsey图中的应用
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2019-09-04 DOI: 10.19086/DA.14351
Matthew Kwan, Lisa Sauermann
{"title":"An algebraic inverse theorem for the quadratic Littlewood-Offord problem, and an application to Ramsey graphs","authors":"Matthew Kwan, Lisa Sauermann","doi":"10.19086/DA.14351","DOIUrl":"https://doi.org/10.19086/DA.14351","url":null,"abstract":"Consider a quadratic polynomial $fleft(xi_{1},dots,xi_{n}right)$ of independent Bernoulli random variables. What can be said about the concentration of $f$ on any single value? This generalises the classical Littlewood--Offord problem, which asks the same question for linear polynomials. As in the linear case, it is known that the point probabilities of $f$ can be as large as about $1/sqrt{n}$, but still poorly understood is the \"inverse\" question of characterising the algebraic and arithmetic features $f$ must have if it has point probabilities comparable to this bound. In this paper we prove some results of an algebraic flavour, showing that if $f$ has point probabilities much larger than $1/n$ then it must be close to a quadratic form with low rank. We also give an application to Ramsey graphs, asymptotically answering a question of Kwan, Sudakov and Tran.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44404767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
Asymptotic Structure for the Clique Density Theorem Clique密度定理的渐近结构
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2019-06-13 DOI: 10.19086/DA.18559
Jaehoon Kim, Hong Liu, O. Pikhurko, M. Sharifzadeh
{"title":"Asymptotic Structure for the Clique Density Theorem","authors":"Jaehoon Kim, Hong Liu, O. Pikhurko, M. Sharifzadeh","doi":"10.19086/DA.18559","DOIUrl":"https://doi.org/10.19086/DA.18559","url":null,"abstract":"The famous Erdős-Rademacher problem asks for the smallest number of $r$-cliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asymptotic value of this extremal function for all $r$ was determined only recently, by Reiher [Annals of Mathematics, 184 (2016) 683--707]. Here we describe the asymptotic structure of all almost extremal graphs. This task for $r=3$ was previously accomplished by Pikhurko and Razborov [Combinatorics, Probability and Computing, 26 (2017) 138--160].","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47408428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3
One-dimensional actions of Higman's group. 希格曼群的一维作用。
IF 1.1 3区 数学
Discrete Analysis Pub Date : 2019-05-02 DOI: 10.19086/DA.11151
C. Rivas, Michele Triestino
{"title":"One-dimensional actions of Higman's group.","authors":"C. Rivas, Michele Triestino","doi":"10.19086/DA.11151","DOIUrl":"https://doi.org/10.19086/DA.11151","url":null,"abstract":"We build a faithful action of Higman's group on the line by homeomorphisms, answering a question of Yves de Cornulier. As a by-product we obtain many quasimorphisms from the Higman group into the reals. We also show that every action by $C^1$-diffeomorphisms of Higman's group on the line or the circle is trivial.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43500870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信