journal: Discrete Mathematics and Applications

Impact Factor: 0.5

Veröffentlicht seit 1. Januar 1991

Discrete Mathematics and Applications

ISSN: 1569-3929

Editor-in-Chief: Andrei M. Zubkov

Über diese Zeitschrift

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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Fachgebiete

Band 33 Heft 4

August 2023

Öffentlich zugänglich 18. August 2023

Frontmatter

Seiten: i-iii

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18. August 2023

On distance-regular graphs Γ of diameter 3 for which Γ₃ is a triangle-free graph

Aleksandr A. Makhnev, Wenbin Guo

Seiten: 199-204

Mehr

Abstract

There exist well-known distance-regular graphs Γ of diameter 3 for which Γ 3 is a triangle-free graph. An example is given by the Johnson graph J (8, 3) with the intersection array {15, 8, 3;1, 4, 9}. The paper is concerned with the problem of the existence of distance-regular graphs Γ with the intersection arrays {78, 50, 9;1, 15, 60} and {174, 110, 18;1, 30, 132} for which Γ 3 is a triangle-free graph.

18. August 2023

Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case

Elena V. Khvorostianskaia

Seiten: 205-217

Mehr

Abstract

We consider a critical Galton – Watson branching process starting with N particles; the number of offsprings is supposed to have the distribution p k =( k + 1) − τ −( k + 2) − τ , k =0, 1, 2, … Limit distributions of the maximal tree size are obtained for the corresponding Galton – Watson forest with N trees and n non-root vertices as N , n → ∞, n / N τ ⩾ C > 0.

18. August 2023

Short complete diagnostic tests for circuits with two additional inputs in some basis

Kirill A. Popkov

Seiten: 219-230

Mehr

Abstract

We prove that any Boolean function in n variables can be modeled by a testable Boolean circuit with two additional inputs in the basis “conjunction, oblique conjunction, disjunction, negation” so that the circuit admits a complete diagnostic test of the length at most 2 n + 3 with respect to stuck-at faults of the type 1 at gate outputs.

18. August 2023

Nonlinearity of functions over finite fields

Vladimir G. Ryabov

Seiten: 231-246

Mehr

Abstract

The nonlinearity and additive nonlinearity of a function are defined as the Hamming distances, respectively, to the set of all affine mappings and to the set of all mappings having nontrivial additive translators. On the basis of the revealed relation between the nonlinearities and the Fourier coefficients of the characters of a function, convenient formulas for nonlinearity evaluation for practically important classes of functions over an arbitrary finite field are found. In the case of a field of even characteristic, similar results were obtained for the additive nonlinearity in terms of the autocorrelation coefficients. The formulas obtained made it possible to present specific classes of functions with maximal possible and high nonlinearity and additive nonlinearity.

18. August 2023

The limit joint distributions of statistics of three tests of the NIST package

Maksim P. Savelov

Seiten: 247-257

Mehr

Abstract

For sequences of independent random variables having a Bernoulli distribution the joint distribution and the limit joint distribution of statistics of three tests of the NIST statistical package («Monobit Test», «Frequency Test within a Block», and «Cumulative Sums Test») are obtained. In the case when two blocks are used in «Frequency Test within a Block», pairwise covariance of these statistics is given.

18. August 2023

On properties of multiaffine predicates on a finite set

Svetlana N. Selezneva

Seiten: 259-267

Mehr

Abstract

We consider predicates on a finite set that are invariant with respect to an affine operation f G , where G is some Abelian group. Such predicates are said to be multiaffine for the group G . Special attention is paid to predicates that are affine for a group G q of addition modulo q = p s , where p is a prime number and s =1. We establish the predicate multiaffinity criterion for a group G q . Then we introduce disjunctive normal forms (DNF) for predicates on a finite set and obtain properties of DNFs of predicates that are multiaffine for a group G q . Finally we show how these properties can be used to design a polynomial algorithm that decides satisfiability of a system of predicates which are multiaffine for a group G q , if predicates are specified by DNF.

18. August 2023

On the universality of product for classes of linear functions of two variables

Andrey A. Voronenko

Seiten: 269-271

Mehr

Abstract

Earlier, the author introduced the concept of a universal function and proved the existence of universal functions for classes of linear k -valued functions of two variables for k ≥ 5 . In this paper, we show that the product modulo k is a universal function for the class of linear k -valued functions of two variables if and only if k = 6l ± 1 .

Band 33 (2023)

Band 32 (2022)

Band 31 (2021)

Band 30 (2020)

Band 29 (2019)

Band 28 (2018)

Band 27 (2017)

Band 26 (2016)

Band 25 (2015)

Band 24 (2014)

Band 23 (2013)

Band 22 (2012)

Band 21 (2011)

Band 20 (2010)

Band 19 (2009)

Band 18 (2008)

Band 17 (2007)

Band 16 (2006)

Band 15 (2005)

Band 14 (2004)

Band 13 (2003)

Band 12 (2002)

Band 11 (2001)

Band 10 (2000)

Band 9 (1999)

Band 8 (1998)

Band 7 (1997)

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Band 5 (1995)

Band 4 (1994)

Band 3 (1993)

Band 2 (1992)

Band 1 (1991)

Journal Impact Factor	0.5	2022, Journal Citation Reports (Clarivate, 2023)
5-year Journal Impact Factor	0.4	2022, Journal Citation Reports (Clarivate, 2023)
Journal Citation Indicator	0.20	2022, Journal Citation Reports (Clarivate, 2023)
CiteScore	0.7	2022, Scopus (Elsevier B.V., 2023)
SCImago Journal Rank	0.265	2022, SJR (Scimago Lab, 2023; Data Source: Scopus)
Source Normalized Impact per Paper	0.912	2022, CWTS Journal Indicators (CWTS B.V., 2023; Data Source: Scopus)
Mathematical Citation Quotient	0.04

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Submission is done electronically by emailing both a PDF file and the source files (LaTeX) to the Editorial Office at dma@mi.ras.ru

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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

(English)

Online ISSN: 1569-3929
Print ISSN: 0924-9265
Typ: Zeitschrift
Sprache: Englisch
Verlag: De Gruyter
Erstveröffentlichung: 1. Januar 1991
Erscheinungsweise: 6 Hefte pro Jahr
Zielgruppe: researchers interested in discrete mathematics and its applications

Discrete Mathematics and Applications

Frontmatter

On distance-regular graphs Γ of diameter 3 for which Γ3 is a triangle-free graph

Abstract

Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case

Abstract

Short complete diagnostic tests for circuits with two additional inputs in some basis

Abstract

Nonlinearity of functions over finite fields

Abstract

The limit joint distributions of statistics of three tests of the NIST package

Abstract

On properties of multiaffine predicates on a finite set

Abstract

On the universality of product for classes of linear functions of two variables

Abstract

On distance-regular graphs Γ of diameter 3 for which Γ₃ is a triangle-free graph