Published since January 1, 1991

Discrete Mathematics and Applications

ISSN: 1569-3929

Editor-in-chief: Andrei M. Zubkov

About this journal

Objective
Discrete Mathematics and Applications provides the latest information on the development of discrete mathematics in Russia to a world-wide readership. The journal contains papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications covers various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.

The journal is published bimonthly, simultaneously with the Russian edition as a cover-to-cover translation. Issues contain, in addition to original articles and reviews in the above-mentioned subject areas, reviews of books published in and outside Russia and information notes. Articles written in the English-language are most welcome!

Topics

Combinatorial analysis
Graph theory
Functional systems theory
Cryptology
Coding
Probabilistic problems of discrete mathematics
Algorithms and their complexity
Combinatorial and computational problems of number theory and of algebra
Number theory
Combinatorics and graph
Probability theory
Statistics

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Original research articles

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Various contributions covering most urgent topics in discrete mathematics
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Volume 32 Issue 3

June 2022

Publicly Available June 15, 2022

Frontmatter

Page range: i-iii

Download PDF

June 15, 2022

Diagnostic tests for discrete functions defined on rings

Grigoriy V. Antyufeev

Page range: 147-153

Abstract

The paper is concerned with sources of faults associated with commutative principal ideal rings. Tables of faults of such sources are known to correspond to Cayley multiplication tables in rings, whose elements are replaced by the values of a Boolean function of these elements. For such rings, the concepts of a diagnostic test and the Shannon function for the length of a diagnostic test are introduced in a natural way. It is shown that if A is a principal ideal ring with only one prime ideal p ≠ A , and if p n = 0 for some n ∈ ℕ, then, for this ring, the Shannon length function of a diagnostic test has the form L diagn ( A , n ) = Θ ( n ). We also define an easily testable functions, i.e., a function with respect to which the order of growth of the length of a diagnostic test with respect to this function is equal to the logarithm of the number of pairwise distinct columns of the table of faults. A link between easily testable functions and column separation of tables of faults for two concrete sources of faults is established.

June 15, 2022

New lower bound for the minimal number of edges of simple uniform hypergraph without the property B_k

Yury A. Demidovich

Page range: 155-176

Abstract

A hypergraph H = ( V , E ) has the property B k if there exists an assignment of two colors to V such that each edge contains at least k vertices of each color. A hypergraph is called simple if every two edges of it have at most one common vertex. We obtain a new lower bound for the minimal number of edges of n -uniform simple hypergraph without the property B k .

June 15, 2022

On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions

Oleg A. Logachev, Sergey N. Fedorov, Valerii V. Yashchenko

Page range: 177-192

Abstract

Let G be the extension of a general affine group by the group of affine functions. We study the action of G on the set of Boolean functions. The action consists in nondegenerate affine transformations of variables and addition of affine Boolean functions. We introduce and examine some parameters of Boolean functions which are invariant with respect to the action of G . These are the amplitude (which is closely related to the nonlinearity), the dimension of a function, and some others. The invariants, together with some additionally proposed notions, could be used to obtain new bounds on cryptographic parameters of Boolean functions, including the maximum nonlinearity of functions in an odd number of variables.

June 15, 2022

On some limit properties for the power series distribution

Yu Miao, Yanyan Tang, Xiaoming Qu, Guangyu Yang

Page range: 193-205

Abstract

In the present paper, we consider random variables with the power series distribution which is often used in the study of the generalized allocation scheme. We establish some asymptotic properties which include law of large numbers, moderate deviation principle, almost sure central limit theorem and the rate of convergence in the local limit theorem. These results supplements results obtained by A. V. Kolchin.

June 15, 2022

Estimates of lengths of shortest nonzero vectors in some lattices. I

Alexander S. Rybakov

Page range: 207-218

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.

Volume 32 (2022)

Volume 31 (2021)

Volume 30 (2020)

Volume 29 (2019)

Volume 28 (2018)

Volume 27 (2017)

Volume 26 (2016)

Volume 25 (2015)

Volume 24 (2014)

Volume 23 (2013)

Volume 22 (2012)

Volume 21 (2011)

Volume 20 (2010)

Volume 19 (2009)

Volume 18 (2008)

Volume 17 (2007)

Volume 16 (2006)

Volume 15 (2005)

Volume 14 (2004)

Volume 13 (2003)

Volume 12 (2002)

Volume 11 (2001)

Volume 10 (2000)

Volume 9 (1999)

Volume 8 (1998)

Volume 7 (1997)

Volume 6 (1996)

Volume 5 (1995)

Volume 4 (1994)

Volume 3 (1993)

Volume 2 (1992)

Volume 1 (1991)

Cite Score	0.5
Journal Citation Indicator	0.17
Mathematical Citation Quotient	0.06
SCImago Journal Rank	0.226
Source Normalized Impact per Paper	0.627

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Editorial

Andrei M. Zubkov; Moscow

Editorial Board
Valery B. Alekseev; Moscow
Vladimir N. Chubarikov; Moscow
Yuri L. Ershov; Novosibirsk
Grigory I. Ivchenko; Moscow
Yurii S. Kharin; Minsk
Vadim V. Kochergin; Moscow
Yuri I. Medvedev; Moscow
Vladimir G. Mikhailov; Moscow
Yuri L. Pavlov; Petrozavodsk
Boris A. Pogorelov; Moscow
Eduard A. Primenko; Moscow
Vladimir N. Sachkov; Moscow
Dmitry A. Shabanov; Moscow
Vladimir A. Vatutin; Moscow

Advisory Board
Vladimir A. Emelichev; Minsk
Yuri L. Ershov; Novosibirsk
Yuri I. Matiyasevich; St. Petersburg
Lev Ya. Savelyev; Novosibirsk
Sergei A. Stepanov; Moscow

(Deutsch)

Online ISSN: 1569-3929
Print ISSN: 0924-9265
Type: Journal
Language: English
Publisher: De Gruyter
First published: January 1, 1991
Publication Frequency: 6 Issues per Year
Audience: researchers interested in discrete mathematics and its applications

Discrete Mathematics and Applications

Frontmatter

Diagnostic tests for discrete functions defined on rings

Abstract

New lower bound for the minimal number of edges of simple uniform hypergraph without the property Bk

Abstract

On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions

Abstract

On some limit properties for the power series distribution

Abstract

Estimates of lengths of shortest nonzero vectors in some lattices. I

Abstract

New lower bound for the minimal number of edges of simple uniform hypergraph without the property B_k