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Moscow Journal of Combinatorics and Number Theory最新文献

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Generalized simultaneous approximation to mlinearly dependent reals 多重线性相关实数的广义同时逼近
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-07-23 DOI: 10.2140/MOSCOW.2019.8.219
Leonhard Summerer
{"title":"Generalized simultaneous approximation to m\u0000linearly dependent reals","authors":"Leonhard Summerer","doi":"10.2140/MOSCOW.2019.8.219","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.219","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2019.8.219","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44820128","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 problem of De Koninck 关于De Koninck的一个问题
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-06-24 DOI: 10.2140/moscow.2021.10.249
Tomohiro Yamada
{"title":"On a problem of De Koninck","authors":"Tomohiro Yamada","doi":"10.2140/moscow.2021.10.249","DOIUrl":"https://doi.org/10.2140/moscow.2021.10.249","url":null,"abstract":"Let $sigma(n)$ and $gamma(n)$ denote the sum of divisors and the product of distinct prime divisors of $n$ respectively. We shall show that, if $nneq 1, 1782$ and $sigma(n)=(gamma(n))^2$, then there exist odd (not necessarily distinct) primes $p, p^prime$ and (not necessarily odd) distinct primes $q_i (i=1, 2, ldots, k)$ such that $p, p^primemidmid n$, $q_i^2midmid n (i=1, 2, ldots, k)$ and $q_1mid sigma(p^2), q_{i+1}midsigma(q_i^2) (i=1, 2, ldots, k-1), p^prime midsigma(q_k^2)$.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48294949","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
A new explicit formula for Bernoulli numbers involving the Euler number 一个新的包含欧拉数的伯努利数显式公式
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-06-13 DOI: 10.31219/osf.io/zkwjc
S. Jha
{"title":"A new explicit formula for Bernoulli numbers involving the Euler number","authors":"S. Jha","doi":"10.31219/osf.io/zkwjc","DOIUrl":"https://doi.org/10.31219/osf.io/zkwjc","url":null,"abstract":"In this brief note, we derive a new explicit formula for Bernoulli numbers in terms of the Stirling numbers of the second kind and the Euler numbers. As a corollary of our result, we obtain an explicit formula for the Euler numbers in terms of the Stirling numbers of the second kind.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47094560","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: 6
Matiyasevich-type identities for hypergeometric Bernoulli polynomials and poly-Bernoulli polynomials 超几何伯努利多项式和poly-Bernoulli多项式的Matiyasevich型恒等式
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-05-20 DOI: 10.2140/MOSCOW.2019.8.137
Ken Kamano
{"title":"Matiyasevich-type identities for hypergeometric Bernoulli polynomials and poly-Bernoulli polynomials","authors":"Ken Kamano","doi":"10.2140/MOSCOW.2019.8.137","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.137","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2019.8.137","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44464483","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
A simple proof of the Hilton–Milnertheorem Hilton–Milner定理的一个简单证明
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-05-20 DOI: 10.2140/MOSCOW.2019.8.97
P. Frankl
{"title":"A simple proof of the Hilton–Milner\u0000theorem","authors":"P. Frankl","doi":"10.2140/MOSCOW.2019.8.97","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.97","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2019.8.97","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49553144","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: 10
Long monochromatic paths and cycles in 2-edge-colored multipartite graphs 2-边色多部分图的长单色路径和循环
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-05-12 DOI: 10.2140/moscow.2020.9.55
J. Balogh, A. Kostochka, Mikhail Lavrov, Xujun Liu
{"title":"Long monochromatic paths and cycles in 2-edge-colored multipartite graphs","authors":"J. Balogh, A. Kostochka, Mikhail Lavrov, Xujun Liu","doi":"10.2140/moscow.2020.9.55","DOIUrl":"https://doi.org/10.2140/moscow.2020.9.55","url":null,"abstract":"We solve four similar problems: For every fixed $s$ and large $n$, we describe all values of $n_1,ldots,n_s$ such that for every $2$-edge-coloring of the complete $s$-partite graph $K_{n_1,ldots,n_s}$ there exists a monochromatic (i) cycle $C_{2n}$ with $2n$ vertices, (ii) cycle $C_{geq 2n}$ with at least $2n$ vertices, (iii) path $P_{2n}$ with $2n$ vertices, and (iv) path $P_{2n+1}$ with $2n+1$ vertices. \u0000This implies a generalization for large $n$ of the conjecture by Gyarfas, Ruszinko, Sarkőzy and Szemeredi that for every $2$-edge-coloring of the complete $3$-partite graph $K_{n,n,n}$ there is a monochromatic path $P_{2n+1}$. An important tool is our recent stability theorem on monochromatic connected matchings.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2020.9.55","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44104346","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: 6
Applications of Siegel’s lemma to a system oflinear forms and its minimal points Siegel引理在线性形式及其极小点系统中的应用
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-04-12 DOI: 10.2140/moscow.2022.11.125
J. Schleischitz
{"title":"Applications of Siegel’s lemma to a system of\u0000linear forms and its minimal points","authors":"J. Schleischitz","doi":"10.2140/moscow.2022.11.125","DOIUrl":"https://doi.org/10.2140/moscow.2022.11.125","url":null,"abstract":"Consider a real matrix $Theta$ consisting of rows $(theta_{i,1},ldots,theta_{i,n})$, for $1leq ileq m$. The problem of making the system linear forms $x_{1}theta_{i,1}+cdots+x_{n}theta_{i,n}-y_{i}$ for integers $x_{j},y_{i}$ small naturally induces an ordinary and a uniform exponent of approximation, denoted by $w(Theta)$ and $widehat{w}(Theta)$ respectively. For $m=1$, a sharp lower bound for the ratio $w(Theta)/widehat{w}(Theta)$ was recently established by Marnat and Moshchevitin. We give a short, new proof of this result upon a hypothesis on the best approximation integer vectors associated to $Theta$. Our conditional result extends to general $m>1$ (but may not be optimal in this case). Moreover, our hypothesis is always satisfied in particular for $m=1, n=2$ and thereby unconditionally confirms a previous observation of Jarn'ik. We formulate our results in the more general context of approximation of subspaces of Euclidean spaces by lattices. We further establish criteria upon which a given number $ell$ of consecutive best approximation vectors are linearly independent. Our method is based on Siegel's Lemma.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49265267","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: 4
On polynomial-time solvable linear Diophantine problems 多项式时间可解线性丢番图问题
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-03-14 DOI: 10.2140/moscow.2019.8.357
I. Aliev
{"title":"On polynomial-time solvable linear Diophantine problems","authors":"I. Aliev","doi":"10.2140/moscow.2019.8.357","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.357","url":null,"abstract":"We obtain a polynomial-time algorithm that, given input (A, b), where A=(B|N) is an integer mxn matrix, m<n, with nonsingular mxm submatrix B and b is an m-dimensional integer vector, finds a nonnegative integer solution to the system Ax=b or determines that no such solution exists, provided that b is located sufficiently \"deep\" in the cone generated by the columns of B. This result improves on some of the previously known conditions that guarantee polynomial-time solvability of linear Diophantine problems.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.357","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44670210","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
Discretized sum-product for large sets 大集合的离散和积
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-01-27 DOI: 10.2140/moscow.2020.9.17
Chang-Pao Chen
{"title":"Discretized sum-product for large sets","authors":"Chang-Pao Chen","doi":"10.2140/moscow.2020.9.17","DOIUrl":"https://doi.org/10.2140/moscow.2020.9.17","url":null,"abstract":"Let $Asubset [1, 2]$ be a $(delta, sigma)$-set with measure $|A|=delta^{1-sigma}$ in the sense of Katz and Tao. For $sigmain (1/2, 1)$ we show that $$ |A+A|+|AA|gtrapprox delta^{-c}|A|, $$ for $c=frac{(1-sigma)(2sigma-1)}{6sigma+4}$. This improves the bound of Guth, Katz, and Zahl for large $sigma$.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2020.9.17","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49646520","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: 5
Linear independence of 1, $mathrm{Li}_1$ and $mathrm{Li}_2$ $mathrm{Li}_1$和$mathrm{Li}_2$的线性无关性
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-01-01 DOI: 10.2140/MOSCOW.2019.8.81
G. Rhin, C. Viola
{"title":"Linear independence of 1, $mathrm{Li}_1$ and $mathrm{Li}_2$","authors":"G. Rhin, C. Viola","doi":"10.2140/MOSCOW.2019.8.81","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.81","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"8 1","pages":"81-96"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2019.8.81","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68081218","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
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