A semigroup variety is a Rees-Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. The collection of all permutative combinatorial Rees-Sushkevich varieties constitutes an incomplete lattice that does not contain the complete join J of all its varieties. The objective of this article is to investigate the subvarieties of J. It is shown that J is locally ...

Gian-Carlo Rota said that “Anyone who has worked with matroids has come away with the conviction that matroids are one of the richest and most useful ideas of our day.” [20] Hassler Whitney introduced the theory of matroids in 1935 and developed a striking number of their basic properties as well as different ways to formulate the notion of a matroid. As more and more connections between matroi...

The existence of incentive-compatible computationally-efficient protocols for combinatorial auctions with decent approximation ratios is the paradigmatic problem in computational mechanism design. It is believed that in many cases good approximations for combinatorial auctions may be unattainable due to an inherent clash between truthfulness and computational efficiency. However, to date, resea...

Mathematical and combinatorial techniques with nonnegative integers are used as computing algorithms for the programs development to apply in artificial intelligence cybersecurity. Methodological advances combinatorics mathematics play a vital role machine learning data analysis intelligence-based cybersecurity protection of systems, devices, networks, from cyber-attacks. In connection these id...

In this article we consider a multicriteria combinatorial problem with ordered MINMIN criteria. We obtain necessary and sufficient conditions of that type of stability to the initial data perturbations for which all lexicographic optima of the original problem are preserved and occurrence of the new ones is allowed. Mathematics subject classification: 90C27, 90C29, 90C31

A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of view. This note consists essentially of definitions and summaries.

The paper presents a course on Combinatorial Algorithms that is based on the drafts of the author that he used while teaching the course in the Department of Informatics and Applied Mathematics of Yerevan State University, Armenia from February 2007 to June 2007.

Some combinatorial results concerning finite decompositions (dissections) of a k-dimensional cube into cubes (respectively, simplexes) of the same dimension are presented in the paper. In connection with such decompositions, the notion of a decomposability number is introduced and the problem of description of all these numbers is discussed. 2000 Mathematics Subject Classification: 52A15, 52B05...

Combinatorial Programs and Efficient Property Testers Artur Czumaj Department of Computer Science New Jersey Institute of Technology University Heights Newark, NJ 07102-1982, USA E-mail: [email protected] Christian Sohler Heinz Nixdorf Institute and Department of Mathematics & Computer Science University of Paderborn D-33095 Paderborn, Germany E-mail: [email protected]

We consider new properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). In particular, we establish an infinite set of Ramanujan-type congruences for the restricted overpartitions known as `-regular overpartitions. This significantly extends the recent work of Shen which focused solely on 3–regular overpartitions and 4–regular o...