发布求助
文献互助 智能选刊 最新文献

Discrete Mathematics and Applications最新文献

筛选
英文 中文
Estimates of lengths of shortest nonzero vectors in some lattices. I 一些格中最短非零向量长度的估计。我
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-06-01 DOI: 10.1515/dma-2022-0018
A. S. Rybakov
{"title":"Estimates of lengths of shortest nonzero vectors in some lattices. I","authors":"A. S. Rybakov","doi":"10.1515/dma-2022-0018","DOIUrl":"https://doi.org/10.1515/dma-2022-0018","url":null,"abstract":"Abstract In 1988, Friese et al. put forward lower estimates for the lengths of shortest nonzero vectors for “almost all” lattices of some families in the dimension 3. In 2004, the author of the present paper obtained a similar result for the dimension 4. Here we give a better estimate for the cardinality of the set of exceptional lattices for which the above estimates are not valid. In the case of dimension 4 we improve the upper estimate for an arbitrary chosen parameter that controls the accuracy of these lower estimates and for the number of exceptions. In this (first) part of the paper, we also prove some auxiliary results, which will be used in the second (main) part of the paper, in which an analogue of A. Friese et al. result will be given for dimension 5.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"207 - 218"},"PeriodicalIF":0.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44995322","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
Completeness criterion with respect to the enumeration closure operator in the three-valued logic 关于三值逻辑中枚举闭包运算符的完备性准则
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI: 10.1515/dma-2022-0010
S. Marchenkov, V. A. Prostov
{"title":"Completeness criterion with respect to the enumeration closure operator in the three-valued logic","authors":"S. Marchenkov, V. A. Prostov","doi":"10.1515/dma-2022-0010","DOIUrl":"https://doi.org/10.1515/dma-2022-0010","url":null,"abstract":"Abstract The enumeration closure operator (the Π-operator) is considered on the set Pk of functions of the k-valued logic. It is proved that, for any k ⩾ 2, any positively precomplete class in Pk is also Π-precomplete. It is also established that there are no other Π-precomplete classes in the three-valued logic.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"105 - 114"},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45194701","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
Some cardinality estimates for the set of correlation-immune Boolean functions 一组相关免疫布尔函数的基数估计
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI: 10.1515/dma-2022-0008
E. Karelina
{"title":"Some cardinality estimates for the set of correlation-immune Boolean functions","authors":"E. Karelina","doi":"10.1515/dma-2022-0008","DOIUrl":"https://doi.org/10.1515/dma-2022-0008","url":null,"abstract":"Abstract Estimates for the cardinality of the set of correlation-immune n-ary Boolean functions with fixed weight are obtained.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"91 - 96"},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45534550","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
Admissible and Bayes decisions with fuzzy-valued losses 具有模糊值损失的容许和贝叶斯决策
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI: 10.1515/dma-2022-0013
A. S. Shvedov
{"title":"Admissible and Bayes decisions with fuzzy-valued losses","authors":"A. S. Shvedov","doi":"10.1515/dma-2022-0013","DOIUrl":"https://doi.org/10.1515/dma-2022-0013","url":null,"abstract":"Abstract Some results of classical statistical decision theory are generalized by means of the theory of fuzzy sets. The concepts of an admissible decision in the restricted sense, an admissible decision in the broad sense, a Bayes decision in the restricted sense, and a Bayes decision in the broad sense are introduced. It is proved that any Bayes decision in the broad sense with positive prior discrete density is admissible in the restricted sense. The class of Bayes decisions is shown to be complete under certain conditions on the loss function. Problems with a finite set of possible states are considered.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"139 - 145"},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42891262","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
Finding periods of Zhegalkin polynomials Zhegalkin多项式的求周期
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI: 10.1515/dma-2022-0012
S. Selezneva
{"title":"Finding periods of Zhegalkin polynomials","authors":"S. Selezneva","doi":"10.1515/dma-2022-0012","DOIUrl":"https://doi.org/10.1515/dma-2022-0012","url":null,"abstract":"Abstract A period of a Boolean function f(x1, …, xn) is a binary n-tuple a = (a1, …, an) that satisfies the identity f(x1 + a1, …, xn + an) = f(x1, …, xn). A Boolean function is periodic if it admits a nonzero period. We propose an algorithm that takes the Zhegalkin polynomial of a Boolean function f(x1, …, xn) as the input and finds a basis of the space of all periods of f(x1, …, xn). The complexity of this algorithm is nO(d), where d is the degree of the function f. As a corollary we show that a basis of the space of all periods of a Boolean function specified by the Zhegalkin polynomial of a bounded degree may be found with complexity which is polynomial in the number of variables.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"129 - 138"},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44438184","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
Some families of closed classes in Pk defined by additive formulas 由加性公式定义的Pk中闭类的一些族
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI: 10.1515/dma-2022-0011
D. G. Meshchaninov
{"title":"Some families of closed classes in Pk defined by additive formulas","authors":"D. G. Meshchaninov","doi":"10.1515/dma-2022-0011","DOIUrl":"https://doi.org/10.1515/dma-2022-0011","url":null,"abstract":"Abstract We analyse closed classes in k-valued logics containing all linear functions modulo k. The classes are determined by divisors d of a number k and canonical formulas for functions. We construct the lattice of all such classes for k = p2, where p is a prime, and construct fragments of the lattice for other composite k.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"115 - 128"},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45586835","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
Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate 具有最小对数增长率的多值逻辑中函数类的连续性
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI: 10.1515/dma-2022-0009
Stepan Alekseevich Komkov
{"title":"Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate","authors":"Stepan Alekseevich Komkov","doi":"10.1515/dma-2022-0009","DOIUrl":"https://doi.org/10.1515/dma-2022-0009","url":null,"abstract":"Abstract We show that in multivalued logic there exist a continual family of pairwise incomparable closed sets with minimal logarithmic growth rate and a continual chain of nested closed sets with minimal logarithmic growth rate. As a corollary we prove that any subset-preserving class in multivalued logic contains a continual chain of nested closed sets and a continual family of pairwise incomparable closed sets such that none of the sets is a subset of any other precomplete class.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"97 - 103"},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49590785","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 site-perimeter of compositions 作品的场地周界
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI: 10.1515/dma-2022-0007
A. Blecher, C. Brennan, A. Knopfmacher
{"title":"The site-perimeter of compositions","authors":"A. Blecher, C. Brennan, A. Knopfmacher","doi":"10.1515/dma-2022-0007","DOIUrl":"https://doi.org/10.1515/dma-2022-0007","url":null,"abstract":"Abstract Compositions of n are finite sequences of positive integers (σi)i=1k $begin{array}{} (sigma_i)_{i = 1}^k end{array} $ such that σ1+σ2+⋯+σk=n. $$begin{array}{} sigma_1+sigma_2+cdots +sigma_k = n. end{array} $$ We represent a composition of n as a bargraph with area n such that the height of the i-th column of the bargraph equals the size of the i-th part of the composition. We consider the site-perimeter which is the number of nearest-neighbour cells outside the boundary of the polyomino. The generating function that counts the total site-perimeter of compositions is obtained. In addition, we rederive the average site-perimeter of a composition by direct counting. Finally we determine the average site-perimeter of a bargraph with a given semi-perimeter.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"75 - 89"},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48468093","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
Variance of the number of cycles of random A-permutation 随机a置换的循环数的方差
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-02-01 DOI: 10.1515/dma-2022-0005
A. L. Yakymiv
{"title":"Variance of the number of cycles of random A-permutation","authors":"A. L. Yakymiv","doi":"10.1515/dma-2022-0005","DOIUrl":"https://doi.org/10.1515/dma-2022-0005","url":null,"abstract":"Abstract We consider random permutations having uniform distribution on the set of all permutations of the n-element set with lengths of cycles belonging to a fixed set A (so-called A-permutations). For some class of sets A the asymptotic formula for the variance of the number of cycles of such permutations is obtained.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"59 - 68"},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43821489","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
A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic 包含Pearson统计量的多项式格式中的一类渐近独立统计量
IF 0.5
Discrete Mathematics and Applications Pub Date : 2022-02-01 DOI: 10.1515/dma-2022-0003
M. P. Savelov
{"title":"A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic","authors":"M. P. Savelov","doi":"10.1515/dma-2022-0003","DOIUrl":"https://doi.org/10.1515/dma-2022-0003","url":null,"abstract":"Abstract We consider a polynomial scheme with N outcomes. The Pearson statistic is the classical one for testing the hypothesis that the probabilities of outcomes are given by the numbers p1, …, pN. We suggest a couple of N − 2 statistics which along with the Pearson statistics constitute a set of N − 1 asymptotically jointly independent random variables, and find their limit distributions. The Pearson statistics is the square of the length of asymptotically normal random vector. The suggested statistics are coordinates of this vector in some auxiliary spherical coordinate system.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"39 - 45"},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49632954","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信