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Moscow Journal of Combinatorics and Number Theory最新文献

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On distance graphs in rational spaces 有理空间中的距离图
Moscow Journal of Combinatorics and Number Theory Pub Date : 2023-01-17 DOI: 10.2140/moscow.2023.12.165
A. Sokolov
{"title":"On distance graphs in rational spaces","authors":"A. Sokolov","doi":"10.2140/moscow.2023.12.165","DOIUrl":"https://doi.org/10.2140/moscow.2023.12.165","url":null,"abstract":"For any positive definite rational quadratic form $q$ of $n$ variables let $G(mathbb{Q}^n, q)$ denote the graph with vertices $mathbb{Q}^n$ and $x, y in mathbb{Q}^n$ connected iff $q(x - y) = 1$. This notion generalises standard Euclidean distance graphs. In this article we study these graphs and show how to find the exact value of clique number of the $G(mathbb{Q}^n, q)$. We also prove rational analogue of the Beckman--Quarles theorem that any unit-preserving mapping of $mathbb{Q}^n$ is an isometry.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45381765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the zeros of the derivatives of certain polynomials 关于某些多项式导数的零点
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-10-15 DOI: 10.2140/moscow.2022.11.205
Toufik Zaïmi
{"title":"On the zeros of the derivatives of certain polynomials","authors":"Toufik Zaïmi","doi":"10.2140/moscow.2022.11.205","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.205","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47863434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Additive properties for sets of polynomial values 多项式值集的可加性
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-10-15 DOI: 10.2140/moscow.2022.11.247
Zhenchao Ge
{"title":"Additive properties for sets of polynomial values","authors":"Zhenchao Ge","doi":"10.2140/moscow.2022.11.247","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.247","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49634527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the size of the product of overlapping families 关于重叠家族的乘积的大小
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-10-15 DOI: 10.2140/moscow.2022.11.237
P. Frankl
{"title":"On the size of the product of overlapping families","authors":"P. Frankl","doi":"10.2140/moscow.2022.11.237","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.237","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46487012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On rational approximations for some values ofarctan(s∕r) for natural s and r, s < r 关于自然s和r, s < r时arctan(s / r)值的有理逼近
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-08-13 DOI: 10.2140/moscow.2022.11.181
V. K. Salikhov, M. G. Bashmakova
{"title":"On rational approximations for some values of\u0000arctan(s∕r) for natural s and r, s < r","authors":"V. K. Salikhov, M. G. Bashmakova","doi":"10.2140/moscow.2022.11.181","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.181","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41587571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the maximum size packings of disks with kissing radius 3 关于接吻半径为3的圆盘的最大尺寸填料
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-05-31 DOI: 10.2140/moscow.2022.11.263
A. Golovanov
{"title":"On the maximum size packings of disks with kissing radius 3","authors":"A. Golovanov","doi":"10.2140/moscow.2022.11.263","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.263","url":null,"abstract":"L´aszl´o Fejes T´oth and Alad´ar Heppes proposed the following generalization of the kissing number problem. Given a ball in R d , consider a family of balls touching it, and another family of balls touching the first family. Find the maximal possible number of balls in this arrangement, provided that no two balls intersect by interiors, and all balls are congruent. They showed that the answer for disks on the plane is 19. They also conjectured that if there are three families of disks instead of two, the answer is 37. In this paper we confirm this conjecture.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48184011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On irrationality measure functions for several real numbers 若干实数的无理数测度函数
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-04-05 DOI: 10.2140/moscow.2022.11.197
V. Rudykh
{"title":"On irrationality measure functions for several real numbers","authors":"V. Rudykh","doi":"10.2140/moscow.2022.11.197","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.197","url":null,"abstract":". For n -tuple α = ( α 1 , . . . , α n ) of pairwise independent numbers we consider permutations of irrationality measure functions ψ α ( t ) = min 1 ≤ q ≤ t || qξ || . Let k ( α ) be the number of infinitely occurring different permutations { σ 1 , . . . , σ k ( α ) } . We prove that the size of n -tuple α with k ( α ) = k is n ≤ + . This result is optimal.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46239493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Exponents of Diophantine approximation in dimension 2 for a general class of numbers 一类一般数的二维丢番图近似的指数
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-03-30 DOI: 10.2140/moscow.2022.11.37
Anthony Poëls
{"title":"Exponents of Diophantine approximation in dimension 2 for a general class of numbers","authors":"Anthony Poëls","doi":"10.2140/moscow.2022.11.37","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.37","url":null,"abstract":". We study the Diophantine properties of a new class of transcendental real numbers which contains, among others, Roy’s extremal numbers, Bugeaud-Laurent Sturmian continued fractions, and more generally the class of Sturmian type numbers. We compute, for each real number ξ of this set, several exponents of Diophantine approximation to the pair ( ξ, ξ 2 ), together with ω ∗ 2 ( ξ ) and b ω ∗ 2 ( ξ ), the so-called ordinary and uniform exponent of approximation to ξ by algebraic numbers of degree ≤ 2. As an application, we get new information on the set of values taken by b ω ∗ 2 at transcendental numbers, and we give a partial answer to a question of Fischler about his exponent β 0 .","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68080729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On Galochkin’s characterization of hypergeometricG-functions 关于超几何G函数的Galochkin刻画
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-03-30 DOI: 10.2140/moscow.2022.11.11
T. Rivoal
{"title":"On Galochkin’s characterization of hypergeometric\u0000G-functions","authors":"T. Rivoal","doi":"10.2140/moscow.2022.11.11","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.11","url":null,"abstract":"G-functions are power series in Q[[z]] solutions of linear differential equations, and whose Taylor coefficients satisfy certain (non)-archimedean growth conditions. In 1929, Siegel proved that every generalized hypergeometric series q+1Fq with rational parameters are G-functions, but rationality of parameters is in fact not necessary for an hypergeometric series to be a G-function. In 1981, Galochkin found necessary and sufficient conditions on the parameters of a q+1Fq series to be a non polynomial G-function. His proof used specific tools in algebraic number theory to estimate the growth of the denominators of the Taylor coefficients of hypergeometric series with algebraic parameters. In this paper, we give a different proof using methods from the theory of arithmetic differential equations, in particular the André-Chudnovsky-Katz Theorem on the structure of the non-zero minimal differential equation satisfied by any given G-function, which is Fuchsian with rational exponents.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45972475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On a conjecture of N. Moshchevitin 论N.莫舍维廷的一个猜想
Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-03-30 DOI: 10.2140/moscow.2022.11.115
Leonhard Summerer
{"title":"On a conjecture of N. Moshchevitin","authors":"Leonhard Summerer","doi":"10.2140/moscow.2022.11.115","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.115","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43942281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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