<abstract xmlns="http://www.w3.org/1999/xhtml"> We enumerate permutations avoiding 1324, 2143, and a third 4-letter pattern τ a step toward the goal of enumerating avoiders for all triples of 4-letter patterns. The enumeration is already known for all but five patterns τ, which are treated in this paper.</abstract>

On permutations avoiding 1324, 2143, and another 4-letter pattern

<abstract xmlns="http://www.w3.org/1999/xhtml"> We enumerate permutations avoiding 1243, 2134, and a third 4-letter pattern τ, a step toward the goal of enumerating avoiders for all triples of 4-letter patterns. The enumeration is already known for all but three patterns τ, which are treated in this paper. </abstract>

On permutations avoiding 1243, 2134, and another 4-letter pattern

<abstract xmlns="http://www.w3.org/1999/xhtml"> We demonstrate an approach for exact sampling of certain discrete combinatorial distributions, which is a hybrid of exact Boltzmann sampling and the recursive method, using probabilistic divide-and-conquer (PDC). The approach specializes to exact Boltzmann sampling in the trivial setting, and specializes to PDC deterministic second half in the first non-trivial application. A large class of examples is given for which this method broadly applies, and several examples are worked out explicitly.</abstract>

Improvements to exact Boltzmann sampling using probabilistic divide-and-conquer and the recursive method

<abstract xmlns="http://www.w3.org/1999/xhtml"> We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f ≼ f ο 1 ο f and it is intra-regular if and only if, for any fuzzy subset f of H, we have f ≼1 ο f ο f ο 1. An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f (resp. f ≼ f ο 1 ο f ο 1) and it is semisimple if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f ο 1. The characterization of regular and intra-regular hypersemigroups in terms of fuzzy subsets are very useful for applications. </abstract>

A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets

AHEAD OF PRINT

Volume 30 (2022): Issue 4 (December 2022)

Volume 30 (2022): Issue 3 (October 2022) Special issue dedicated to 70th anniversary of prof. Peter Tallos

Volume 30 (2022): Issue 2 (August 2022)

Volume 30 (2022): Issue 1 (June 2022)

Volume 29 (2020): Issue 1 (December 2020)

Volume 28 (2019): Issue 1 (October 2019)

Volume 27 (2018): Issue 2 (August 2018)

Volume 27 (2018): Issue 1 (July 2018)

Volume 26 (2017): Issue 1 (June 2017)

Volume 25 (2015): Issue 2 (December 2015)

Volume 25 (2015): Issue 1 (September 2015)

Pure Mathematics and Applications

 Pure Mathematics and Applications - section Algebra and Theoretical Computer Science - publishes original high quality articles of international relevance in the two disciplines of algebra and theoretical computer science. Specific topics include (but are not limited to) group and semigroup theory, commutative algebra, computational algebra, poset and lattice theory, linear algebra, theory of automata and formal languages, computational complexity, analysis of algorithms, game theory. In particular, articles in which interactions between algebra and theoretical computer science play a relevant role (i.e. techniques of either discipline are fundamental in obtaining results of the other) will be privileged. As a natural consequence of this fact, one of the disciplines which are more relevant to the journal is discrete mathematics, and more specifically enumerative and algebraic combinatorics, graph theory, discrete tomography, random and exhaustive generation, combinatorial order theory, bioinformatics, matroid theory, combinatorics on words.Papers about high quality applications of combinatorial methods to computer science (especially algorithms, data structures, and criptography), or special issues, completely devoted to a certain contemporary topic of high interest, are also published.  Pure Mathematics and Applications - section Mathematics of Optimization - publishes original research works, surveys, historical and biographical articles primarily on mathematics of optimization. Papers about high quality applications of mathematical methods to decision sciences (especially operations research, economics, games and control theory, actuarial and financial mathematics), or special issues, completely devoted to a certain contemporary topic of high interest are also published.  The journal contains two sections - one devoted to Algebra and Theoretical Computer Science, and second to Mathematics of Optimization. The published articles of the first section focus on algebra and theoretical computer science, with interactions between algebra and theoretical computer science in particular. The second section publishes research works, surveys, historical and biographical articles primarily on mathematics of optimization.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.  Target group  researchers in the fields of algebra and theoretical computer science 