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Moscow Journal of Combinatorics and Number Theory最新文献

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Positive semigroups and generalized Frobenius numbers over totally real number fields 全实数域上的正半群和广义Frobenius数
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-11-19 DOI: 10.2140/moscow.2020.9.29
L. Fukshansky, Yingqi Shi
{"title":"Positive semigroups and generalized Frobenius numbers over totally real number fields","authors":"L. Fukshansky, Yingqi Shi","doi":"10.2140/moscow.2020.9.29","DOIUrl":"https://doi.org/10.2140/moscow.2020.9.29","url":null,"abstract":"Frobenius problem and its many generalizations have been extensively studied in several areas of mathematics. We study semigroups of totally positive algebraic integers in totally real number fields, defining analogues of the Frobenius numbers in this context. We use a geometric framework recently introduced by Aliev, De Loera and Louveaux to produce upper bounds on these Frobenius numbers in terms of a certain height function. We discuss some properties of this function, relating it to absolute Weil height and obtaining a lower bound in the spirit of Lehmer's conjecture for algebraic vectors satisfying some special conditions. We also use a result of Borosh and Treybig to obtain bounds on the size of representations and number of elements of bounded height in such positive semigroups of totally real algebraic integers.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2020.9.29","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43020807","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
A Convexity Criterion for Unique Ergodicity of Interval Exchange Transformations 区间交换变换唯一遍历性的凸性判据
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-11-13 DOI: 10.2140/MOSCOW.2020.9.51
René Rühr
{"title":"A Convexity Criterion for Unique Ergodicity of Interval Exchange Transformations","authors":"René Rühr","doi":"10.2140/MOSCOW.2020.9.51","DOIUrl":"https://doi.org/10.2140/MOSCOW.2020.9.51","url":null,"abstract":"A criterion for unique ergodicity for points of a curve in the space of interval exchange transformation is given.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2020.9.51","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68080655","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
Counting formulas for CM-types CM类型的计数公式
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-10-11 DOI: 10.2140/moscow.2019.8.343
Masanari Kida
{"title":"Counting formulas for CM-types","authors":"Masanari Kida","doi":"10.2140/moscow.2019.8.343","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.343","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.343","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46930094","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
On the domination number of a graph defined by containment 由包含定义的图的支配数
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-10-11 DOI: 10.2140/moscow.2019.8.379
P. Frankl
{"title":"On the domination number of a graph defined by containment","authors":"P. Frankl","doi":"10.2140/moscow.2019.8.379","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.379","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.379","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41675960","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
Correction to the article Intersection theoremsfor (−1,0,1)-vectors and s-cross-intersecting families 对（−1,0,1）-向量和s-交叉族的交集理论一文的修正
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-10-11 DOI: 10.2140/moscow.2019.8.385
P. Frankl, A. Kupavskii
{"title":"Correction to the article Intersection theorems\u0000for (−1,0,1)-vectors and s-cross-intersecting families","authors":"P. Frankl, A. Kupavskii","doi":"10.2140/moscow.2019.8.385","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.385","url":null,"abstract":"In this paper we study two directions of extending the classical ErdH os-Ko-Rado theorem which states that any family of $k$-element subsets of the set $[n] = {1,ldots,n}$ in which any two sets intersect, has cardinality at most ${n-1choose k-1}$. \u0000In the first part of the paper we study the families of ${0,pm 1}$-vectors. Denote by $mathcal L_k$ the family of all vectors $mathbf v$ from ${0,pm 1}^n$ such that $langlemathbf v,mathbf vrangle = k$. For any $k$ and $l$ and sufficiently large $n$ we determine the maximal size of the family $mathcal Vsubset mathcal L_k$ such that for any $mathbf v,mathbf win mathcal V$ we have $langle mathbf v,mathbf wranglege l$. We find some exact values of this function for all $n$ for small values of $k$. \u0000In the second part of the paper we study cross-intersecting pairs of families. We say that two families are $mathcal A, mathcal B$ are textit{$s$-cross-intersecting}, if for any $Ainmathcal A,Bin mathcal B$ we have $|Acap B|ge s$. We also say that a set family $mathcal A$ is textit{$t$-intersecting}, if for any $A_1,A_2in mathcal A$ we have $|A_1cap A_2|ge t$. For a pair of nonempty $s$-cross-intersecting $t$-intersecting families $mathcal A,mathcal B$ of $k$-sets, we determine the maximal value of $|mathcal A|+|mathcal B|$ for $n$ sufficiently large. \u0000If the nonempty families $mathcal A,mathcal B$ are $s$-cross-intersecting (and the $t$-intersecting condition is omitted), then we determine the maximum of $|mathcal A|+|mathcal B|$ for all $n$. This generalizes a result of Hilton and Milner, who determined the maximum of $|mathcal A|+|mathcal B|$ for nonempty $1$-cross-intersecting families.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.385","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43572365","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
Paramodular forms of level 16 and supercuspidal representations 16级的副模形式和超尖叶表示
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-10-11 DOI: 10.2140/moscow.2019.8.289
C. Poor, Ralf Schmidt, D. Yuen
{"title":"Paramodular forms of level 16 and supercuspidal representations","authors":"C. Poor, Ralf Schmidt, D. Yuen","doi":"10.2140/moscow.2019.8.289","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.289","url":null,"abstract":"This work bridges the abstract representation theory of GSp(4) with recent computational techniques. We construct four examples of paramodular newforms whose associated automorphic representations have local representations at p = 2 that are supercuspidal. We classify all relevant irreducible, admissible, supercuspidal representations of GSp(4,Q2), and show that our examples occur at the lowest possible paramodular level, 16. The required theoretical and computational techniques include paramodular newform theory, Jacobi restriction, bootstrapping and Borcherds products.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.289","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48732565","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
The sum-of-digits function on arithmetic progressions 等差数列上的数字和函数
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-09-19 DOI: 10.2140/moscow.2020.9.43
Lukas Spiegelhofer, T. Stoll
{"title":"The sum-of-digits function on arithmetic progressions","authors":"Lukas Spiegelhofer, T. Stoll","doi":"10.2140/moscow.2020.9.43","DOIUrl":"https://doi.org/10.2140/moscow.2020.9.43","url":null,"abstract":"Let $s_2$ be the sum-of-digits function in base $2$, which returns the number of non-zero binary digits of a nonnegative integer $n$. We study $s_2$ alon g arithmetic subsequences and show that --- up to a shift --- the set of $m$-tuples of integers that appear as an arithmetic subsequence of $s_2$ has full complexity.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2020.9.43","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42220469","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 dynamical Borel–Cantelli lemma viaimprovements to Dirichlet’s theorem 一个动态Borel–Cantelli引理及其对Dirichlet定理的改进
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-09-18 DOI: 10.2140/moscow.2020.9.101
D. Kleinbock, Shucheng Yu
{"title":"A dynamical Borel–Cantelli lemma via\u0000improvements to Dirichlet’s theorem","authors":"D. Kleinbock, Shucheng Yu","doi":"10.2140/moscow.2020.9.101","DOIUrl":"https://doi.org/10.2140/moscow.2020.9.101","url":null,"abstract":"Let $Xcong operatorname{SL}_2(mathbb R)/operatorname{SL}_2(mathbb Z)$ be the space of unimodular lattices in $mathbb R^2$, and for any $rge 0$ denote by $K_rsubset X$ the set of lattices such that all its nonzero vectors have supremum norm at least $e^{-r}$. These are compact nested subset{s} of $X$, with $K_0 = {bigcap}_{r}K_r$ being the union of two closed horocycles. We use an explicit second moment formula for the Siegel transform of the indicator functions of squares in $mathbb R^2$ centered at the origin to derive an asymptotic formula for the volume of sets $K_r$ as $rto 0$. Combined with a zero-one law for the set of the $psi$-Dirichlet numbers established by Kleinbock and Wadleigh, this gives a new dynamical Borel-Cantelli lemma for the geodesic flow on $X$ with respect to the family of shrinking targets ${K_r}$.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2020.9.101","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46200975","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: 8
On the distribution of values of Hardy’sZ-functions in short intervals, II : The q-aspect 哈迪z函数值在短区间内的分布，II: q方面
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-07-23 DOI: 10.2140/MOSCOW.2019.8.229
Ramdin Mawia
{"title":"On the distribution of values of Hardy’s\u0000Z-functions in short intervals, II : The q-aspect","authors":"Ramdin Mawia","doi":"10.2140/MOSCOW.2019.8.229","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.229","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.2019.8.229","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46822906","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
The mean square discrepancy in the circle problem 圆问题中的均方差
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-07-23 DOI: 10.2140/MOSCOW.2019.8.263
S. Gonek, A. Iosevich
{"title":"The mean square discrepancy in the circle problem","authors":"S. Gonek, A. Iosevich","doi":"10.2140/MOSCOW.2019.8.263","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.263","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.2019.8.263","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49408507","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
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