<abstract xmlns="http://www.w3.org/1999/xhtml">We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function. Also, we present generalizations of some familiar identities and connection between these types of Bernoulli, Euler, and Genocchi polynomials. Moreover, we establish new analogues of the Euler identity for degenerate Bernoulli polynomials and numbers.</abstract>

New degenerate Bernoulli, Euler, and Genocchi polynomials

<abstract xmlns="http://www.w3.org/1999/xhtml">Let 𝒯(<italic>k</italic>)<italic>n</italic> denote the set of <italic>k</italic>-Stirling permutations having <italic>n</italic> distinct letters. Here, we consider the number of steps required (i.e., <italic>pushes</italic>) to rearrange the letters of a member of 𝒯(<italic>k</italic>)<italic>n</italic> so that they occur in non-decreasing order. We find recurrences for the joint distribution on 𝒯(<italic>k</italic>)<italic>n</italic> for the statistics recording the number of levels (i.e., occurrences of equal adjacent letters) and pushes. When <italic>k</italic> = 2, an explicit formula for the ordinary generating function of this distribution is also found. In order to do so, we determine the <italic>LU</italic>-decomposition of a certain infinite matrix having polynomial entries which enables one to compute explicitly the inverse matrix.</abstract>

Counting Stirling permutations by number of pushes

<abstract xmlns="http://www.w3.org/1999/xhtml">The area of S-Motzkin paths (bijective to ternary trees) is calculated using the kernel method by enumerating these (partial) paths with fixed end-point resp. starting point.</abstract>

Enumeration of S-Motzkin paths from left to right and from right to left: a kernel method approach

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 

Pure Mathematics and Applications

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

New degenerate Bernoulli, Euler, and Genocchi polynomials

Counting Stirling permutations by number of pushes

Enumeration of S-Motzkin paths from left to right and from right to left: a kernel method approach

Search

All Volumes and Issues in this Journal