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Discrete Mathematics and Applications最新文献

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On scatter properties of modular addition operation over imprimitivity systems of the translation group of the binary vector space 二元向量空间平移群非基系统上模加法运算的散射性质
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-06-01 DOI: 10.1515/dma-2023-0013
D. A. Burov
{"title":"On scatter properties of modular addition operation over imprimitivity systems of the translation group of the binary vector space","authors":"D. A. Burov","doi":"10.1515/dma-2023-0013","DOIUrl":"https://doi.org/10.1515/dma-2023-0013","url":null,"abstract":"Abstract We study scatter properties of the modular addition operation for imprimitivity systems of the translation group of the binary vector space Vn = {0, 1}n. We describe all the subspaces of the space Vn that induce imprimitivity systems with worst possible scatter by the modular addition operation.","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":"45068167","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
On the equality problem of finitely generated classes of exponentially-polynomial functions 有限生成类指数多项式函数的等式问题
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-06-01 DOI: 10.1515/dma-2023-0015
S. Marchenkov
{"title":"On the equality problem of finitely generated classes of exponentially-polynomial functions","authors":"S. Marchenkov","doi":"10.1515/dma-2023-0015","DOIUrl":"https://doi.org/10.1515/dma-2023-0015","url":null,"abstract":"Abstract We consider the class EPℕ of exponentially-polynomial functions which can be obtained by arbitrary superpositions of the constants 0, 1 and arithmetic operations of addition, multiplication, and powering. For this class, we solve the algorithmic equality problem of two functions that assume a finite number of values. Next, this class is restricted to the class PEPℕ, in which the function xy is replaced by a sequence of functions { pix $begin{array}{} displaystyle p_i^x end{array}$}, where p0, p1, … are all prime numbers. For the class PEPℕ, the problem of membership of a function to a finitely generated class is effectively reduced to the equality problem of two functions. In turn, the last problem is effectively solved for the set of all one-place PEPℕ-functions.","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":"45958357","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
Fault-tolerant resolvability of some graphs of convex polytopes 一些凸多面体图的容错可分解性
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-06-01 DOI: 10.1515/dma-2023-0016
S. Sharma, H. Raza, V. K. Bhat
{"title":"Fault-tolerant resolvability of some graphs of convex polytopes","authors":"S. Sharma, H. Raza, V. K. Bhat","doi":"10.1515/dma-2023-0016","DOIUrl":"https://doi.org/10.1515/dma-2023-0016","url":null,"abstract":"Abstract The fault-tolerant resolvability is an extension of metric resolvability in graphs with several intelligent systems applications, for example, network optimization, robot navigation, and sensor networking. The graphs of convex polytopes, which are rotationally symmetric, are essential in intelligent networks due to the uniform rate of data transformation to all nodes. A resolving set is an ordered set 𝕎 of vertices of a connected graph G in which the vector of distances to the vertices in 𝕎 uniquely determines all the vertices of the graph G. The minimum cardinality of a resolving set of G is known as the metric dimension of G. If 𝕎 ∖ ρ is also a resolving set for each ρ in 𝕎. In that case, 𝕎 is said to be a fault-tolerant resolving set. The fault-tolerant metric dimension of G is the minimum cardinality of such a set 𝕎. The metric dimension and the fault-tolerant metric dimension for three families of convex polytope graphs are studied. Our main results affirm that three families, as mentioned above, have constant fault-tolerant resolvability structures.","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":"46614530","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
Mutually Orthogonal Latin Squares as Group Transversals 作为群截线的相互正交的拉丁正方形
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0010
R. Pradhan, V. K. Jain
{"title":"Mutually Orthogonal Latin Squares as Group Transversals","authors":"R. Pradhan, V. K. Jain","doi":"10.1515/dma-2023-0010","DOIUrl":"https://doi.org/10.1515/dma-2023-0010","url":null,"abstract":"Abstract In this paper, we give a method to determine a complete set of mutually orthogonal Latin squares of order m, where m is an odd prime or power of a prime, as a group transversal of a Frobenius group.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42166851","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
Criteria for maximal nonlinearity of a function over a finite field 有限域上函数最大非线性的判据
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0012
V. G. Ryabov
{"title":"Criteria for maximal nonlinearity of a function over a finite field","authors":"V. G. Ryabov","doi":"10.1515/dma-2023-0012","DOIUrl":"https://doi.org/10.1515/dma-2023-0012","url":null,"abstract":"Abstract An n-place function over a field with q elements is called maximally nonlinear if it has the greatest nonlinearity among all such functions. Criteria and necessary conditions for maximal nonlinearity are obtained, which imply that, for even n, the maximally nonlinear functions are bent functions, but, for q > 2, the known families of bent functions are not maximally nonlinear. For an arbitrary finite field, a relationship between the Hamming distances from a function to all affine mappings and the Fourier spectra of the nontrivial characters of the function are found.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42932067","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
Decomposition of polynomials using the shift-composition operation 多项式的移位合成分解
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0009
V. Nozdrunov
{"title":"Decomposition of polynomials using the shift-composition operation","authors":"V. Nozdrunov","doi":"10.1515/dma-2023-0009","DOIUrl":"https://doi.org/10.1515/dma-2023-0009","url":null,"abstract":"Abstract V. I. Solodovnikov had employed the shift-composition operation to investigate homomorphisms of shift registers into linear automata; in his papers, conditions for the absence of nontrivial inner homomorphisms of shift registers were derived. An essential role was played by the condition of linearity of the left component of the shift-composition operation in the corresponding polynomial decomposition. In this paper we consider the case where the left component is a function belonging to a wider class, which includes the class of linear functions.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44534856","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
Explicit basis for admissible rules in K-saturated tabular logics K饱和表逻辑中可容许规则的显式基
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0011
V. V. Rimatskiĭ
{"title":"Explicit basis for admissible rules in K-saturated tabular logics","authors":"V. V. Rimatskiĭ","doi":"10.1515/dma-2023-0011","DOIUrl":"https://doi.org/10.1515/dma-2023-0011","url":null,"abstract":"Abstract We construct an explicit finite basis for admissible rules in K-saturated tabular logics that extend the logic Grz.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48169772","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
On the existence of special nonlinear invariants for round functions of XSL-ciphers XSL密码的圆函数的特殊非线性不变量的存在性
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0007
D. Burov
{"title":"On the existence of special nonlinear invariants for round functions of XSL-ciphers","authors":"D. Burov","doi":"10.1515/dma-2023-0007","DOIUrl":"https://doi.org/10.1515/dma-2023-0007","url":null,"abstract":"Abstract Nonlinear invariants of round transformations in XSL-schemes are studied. The emphasis is on invariants which may be found by means of the approach suggested at the conference ASIACRYPT 2016. Some known results on the inertia groups of decomposable functions are used to describe conditions on S-boxes and matrices of XSL-schemes which are necessary for the existence of such invariants. It is shown that for a number of schemes these conditions are not satisfied.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42661238","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
Frontmatter 头版头条
Discrete Mathematics and Applications Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-frontmatter2
{"title":"Frontmatter","authors":"","doi":"10.1515/dma-2023-frontmatter2","DOIUrl":"https://doi.org/10.1515/dma-2023-frontmatter2","url":null,"abstract":"","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134949962","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
Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants 子体几何分布随机环境中分支过程大偏差的渐近局部概率
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0008
Konstantin Yu. Denisov
{"title":"Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants","authors":"Konstantin Yu. Denisov","doi":"10.1515/dma-2023-0008","DOIUrl":"https://doi.org/10.1515/dma-2023-0008","url":null,"abstract":"Abstract We consider the branching process Zn=Xn,1+⋯+XnZn−1 $ Z_{n} =X_{n, 1} + dotsb +X_{nZ_{n-1}} $, in random environmentsη, where η is a sequence of independent identically distributedvariables, for fixed η the random variables Xi, j areindependent, have the geometric distribution. We suppose that the associated random walk Sn=ξ1+⋯+ξn $ S_n = xi_1 + dotsb + xi_n $ has positive meanμ,0 < h<h+satisfies the right-hand Cramer’s condition Eexp(hξi) < ∞ for, some h+. Under theseassumptions, we find the asymptotic representation for local probabilities P(Zn=⌊exp(θ n)⌋) for θ ∈ [θ1, θ2]⊂</given−names><x> </x><surname>(μ;μ+) and someμ+.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45029747","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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