Discrete Mathematics and Applications最新文献_第2页

On small distance-regular graphs with the intersection arrays {mn − 1, (m − 1)(n + 1), n − m + 1; 1, 1, (m − 1)(n + 1)} 在具有交集阵列 {mn - 1, (m - 1)(n + 1), n - m + 1; 1, 1, (m - 1)(n + 1)} 的小型距离不规则图上

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0025

A. Makhnev, M. P. Golubyatnikov

{"title":"On small distance-regular graphs with the intersection arrays {mn − 1, (m − 1)(n + 1), n − m + 1; 1, 1, (m − 1)(n + 1)}","authors":"A. Makhnev, M. P. Golubyatnikov","doi":"10.1515/dma-2023-0025","DOIUrl":"https://doi.org/10.1515/dma-2023-0025","url":null,"abstract":"Abstract Let Γ be a diameter 3 distance-regular graph with a strongly regular graph Γ3, where Γ3 is the graph whose vertex set coincides with the vertex set of the graph Γ and two vertices are adjacent whenever they are at distance 3 in the graph Γ. Computing the parameters of Γ3 by the intersection array of the graph Γ is considered as the direct problem. Recovering the intersection array of the graph Γ by the parameters of Γ3 is referred to as the inverse problem. The inverse problem for Γ3 has been solved earlier by A. A. Makhnev and M. S. Nirova. In the case where Γ3 is a pseudo-geometric graph of a net, a series of admissible intersection arrays has been obtained: {c2(u2 − m2) + 2c2m − c2 − 1, c2(u2 − m2), (c2 − 1)(u2 − m2) + 2c2m − c2; 1, c2, u2 − m2} (A. A. Makhnev, Wenbin Guo, M. P. Golubyatnikov). The cases c2 = 1 and c2 = 2 have been examined by A. A. Makhnev, M. P. Golubyatnikov and A. A. Makhnev, M. S. Nirova, respectively. In this paper in the class of graphs with the intersection arrays {mn − 1, (m − 1)(n + 1)}, {n − m + 1}; 1, 1, (m − 1)(n + 1)} all admissible intersection arrays for {3 ≤ m ≤ 13} are found: {20,16,5; 1, 1,16}, {39,36,4; 1, 1,36}, {55,54,2; 1, 2,54}, {90,84,7; 1, 1,84}, {220,216,5; 1, 1,216}, {272,264,9; 1, 1,264} and {350,336,15; 1, 1,336}. It is demonstrated that graphs with the intersection arrays {20,16,5; 1, 1,16}, {39,36,4; 1, 1,36} and {90,84,7; 1, 1,84} do not exist.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139331533","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

Nonlinearity of functions over finite fields 有限域上函数的非线性

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0021

V. G. Ryabov

引用次数: 0

Short complete diagnostic tests for circuits with two additional inputs in some basis 在某些基础上对具有两个附加输入的电路进行完整的短路诊断测试

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0020

K. A. Popkov

引用次数: 0

On properties of multiaffine predicates on a finite set 关于有限集上多仿射谓词的性质

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0023

S. Selezneva

引用次数: 0

Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case Galton最大树大小的极限定理 – 危急情况下的Watson森林

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0019

Elena V. Khvorostianskaia

引用次数: 0

The limit joint distributions of statistics of three tests of the NIST package NIST软件包三次测试统计的极限联合分布

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0022

Maksim P. Savelov

引用次数: 0

On distance-regular graphs Γ of diameter 3 for which Γ3 is a triangle-free graph 关于直径为3的距离正则图Γ，其中Γ3是无三角形图

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0018

A. Makhnev, Wenbin Guo

引用次数: 0

On the universality of product for classes of linear functions of two variables 关于两变量线性函数类乘积的普适性

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0024

A. A. Voronenko

引用次数: 0

Frontmatter 头版头条

Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-frontmatter4

引用次数: 0

On a number of particles in a marked set of cells in a general allocation scheme 关于一般分配方案中标记单元集中的多个粒子

IF 0.5

Discrete Mathematics and Applications Pub Date : 2023-06-01 DOI: 10.1515/dma-2023-0014

A. Chuprunov

{"title":"On a number of particles in a marked set of cells in a general allocation scheme","authors":"A. Chuprunov","doi":"10.1515/dma-2023-0014","DOIUrl":"https://doi.org/10.1515/dma-2023-0014","url":null,"abstract":"Abstract In a generalized allocation scheme of n particles over N cells we consider the random variable ηn,N(K) which is the number of particles in a given set consisting of K cells. We prove that if n, K, N → ∞, then under some conditions random variables ηn,N(K) are asymptotically normal, and under another conditions ηn,N(K) converge in distribution to a Poisson random variable. For the case when N → ∞ and n is a fixed number, we find conditions under which ηn,N(K) converge in distribution to a binomial random variable with parameters n and s = KN $begin{array}{} displaystyle frac{K}{N} end{array}$, 0 < K < N, multiplied by a integer coefficient. It is shown that if for a generalized allocation scheme of n particles over N cells with random variables having a power series distribution defined by the function B(β) = ln(1 − β) the conditions n, N, K → ∞, KN $begin{array}{} displaystyle frac{K}{N} end{array}$ → s, N = γ ln(n) + o(ln(n)), where 0 < s < 1, 0 < γ < ∞, are satisfied, then distributions of random variables ηn,N(K)n $begin{array}{} displaystyle frac{eta_{n,N}(K)}{n} end{array}$ converge to a beta-distribution with parameters sγ and (1 − s)γ.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47885290","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