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Moscow Journal of Combinatorics and Number Theory最新文献

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Lattices with exponentially large kissing numbers 具有指数级大接吻数的晶格
Moscow Journal of Combinatorics and Number Theory Pub Date : 2018-02-03 DOI: 10.2140/MOSCOW.2019.8.163
S. Vladut
{"title":"Lattices with exponentially large kissing numbers","authors":"S. Vladut","doi":"10.2140/MOSCOW.2019.8.163","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.163","url":null,"abstract":"We construct a sequence of lattices ${L_{n_i}subset mathbb R^{n_i}}$ for $n_ilongrightarrowinfty$, with exponentially large kissing numbers, namely, $log_2tau(L_{n_i})> 0.0338cdot n_i -o(n_i)$. We also show that the maximum lattice kissing number $ tau^l_{n}$ in $n$ dimensions verifies $log_2tau^l_{n}> 0.0219cdot n -o(n)$.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2019.8.163","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68081177","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: 17
Embeddings of weighted graphs in Erdős-typesettings 加权图在Erdõs排版中的嵌入
Moscow Journal of Combinatorics and Number Theory Pub Date : 2017-12-11 DOI: 10.2140/moscow.2019.8.117
David Soukup
{"title":"Embeddings of weighted graphs in Erdős-type\u0000settings","authors":"David Soukup","doi":"10.2140/moscow.2019.8.117","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.117","url":null,"abstract":"Many recent results in combinatorics concern the relationship between the size of a set and the number of distances determined by pairs of points in the set. One extension of this question considers configurations within the set with a specified pattern of distances. In this paper, we use graph-theoretic methods to prove that a sufficiently large set $E$ must contain at least $C_G|E|$ distinct copies of any given weighted tree $G$, where $C_G$ is a constant depending only on the graph $G$.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.117","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45443134","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
Sets of inhomogeneous linear forms can be not isotropically winning 非齐次线性形式的集合不能各向同性获胜
Moscow Journal of Combinatorics and Number Theory Pub Date : 2017-11-16 DOI: 10.2140/moscow.2019.8.3
N. Dyakova
{"title":"Sets of inhomogeneous linear forms can be not isotropically winning","authors":"N. Dyakova","doi":"10.2140/moscow.2019.8.3","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.3","url":null,"abstract":"We give an example of irrational vector $pmb{theta} in mathbb{R}^2$ such that the set $Bad_{pmb{theta}} := {(eta_1,eta_2): inf_{xinmathbb{N}} x^{frac{1}{2}} max_{i=1,2} |x theta_i-eta_i|>0}$ is not absolutely winning with respect to McMullen's game.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49060478","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
Identity involving symmetric sums of regularized multiple zeta-star values 正则化多个ζ星值的对称和的恒等式
Moscow Journal of Combinatorics and Number Theory Pub Date : 2017-11-06 DOI: 10.2140/moscow.2019.8.125
T. Machide
{"title":"Identity involving symmetric sums of regularized multiple zeta-star values","authors":"T. Machide","doi":"10.2140/moscow.2019.8.125","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.125","url":null,"abstract":"An identity involving symmetric sums of regularized multiple zeta-star values of harmonic type was proved by Hoffman. In this paper, we prove an identity of shuffle type. We use Bell polynomials appearing in the study of set partitions to prove the identity.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.125","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46064288","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
Convex sequences may have thin additive bases 凸序列可能具有薄的加性基
Moscow Journal of Combinatorics and Number Theory Pub Date : 2017-08-16 DOI: 10.2140/moscow.2019.8.43
I. Ruzsa, D. Zhelezov
{"title":"Convex sequences may have thin additive bases","authors":"I. Ruzsa, D. Zhelezov","doi":"10.2140/moscow.2019.8.43","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.43","url":null,"abstract":"For a fixed $c > 0$ we construct an arbitrarily large set $B$ of size $n$ such that its sum set $B+B$ contains a convex sequence of size $cn^2$, answering a question of Hegarty.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.43","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48213301","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: 3
Some remarks on the asymmetric sum-product phenomenon 关于非对称和积现象的几点评述
Moscow Journal of Combinatorics and Number Theory Pub Date : 2017-05-26 DOI: 10.2140/moscow.2019.8.15
I. Shkredov
{"title":"Some remarks on the asymmetric sum-product phenomenon","authors":"I. Shkredov","doi":"10.2140/moscow.2019.8.15","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.15","url":null,"abstract":"Using some new observations connected to higher energies, we obtain quantitative lower bounds on $max{|AB|, |A+C| }$ and $max{|(A+alpha)B|, |A+C|}$, $alpha neq 0$ in the regime when the sizes of finite subsets $A,B,C$ of a field differ significantly.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.15","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43085282","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: 24
Admissible endpoints of gaps in the Lagrange spectrum 拉格朗日谱间隙的容许端点
Moscow Journal of Combinatorics and Number Theory Pub Date : 2017-04-26 DOI: 10.2140/moscow.2019.8.47
D. Gayfulin
{"title":"Admissible endpoints of gaps in the Lagrange spectrum","authors":"D. Gayfulin","doi":"10.2140/moscow.2019.8.47","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.47","url":null,"abstract":"We call a positive real number $lambda$ admissible if it belongs to the Lagrange spectrum and there exists an irrational number $alpha$ such that $mu(alpha)=lambda$. Here $mu(alpha)$ denotes the Lagrange constant of $alpha$ - maximal real number $c$ such that $forall varepsilon>0$ the inequality $|alpha-frac{p}{q}|lefrac{1}{(c-varepsilon)q^2}$ has infinitely many solutions for relatively prime $p$ and $q$. In this paper we establish a necessary and sufficient condition of admissibility of the Lagrange spectrum element and construct an infinite series of not admissible numbers.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.47","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44363737","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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