Related papers: A Bibliography of Combinators
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
Invention has been commonly conceptualized as a search over a space of combinatorial possibilities. Despite the existence of a rich literature, spanning a variety of disciplines, elaborating on the recombinant nature of invention, we lack a…
We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club…
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
We develop certain combinatorial tools for the study of discriminants of general systems of polynomial equations. Applying these tools in a sequel paper, we completely classify components of such discriminants, generalizing the classical…
I take a quick overview at the recent development of combinatorics and its current directions, as a discipline in its own right, as part of mathematics, and as part of science and wider society.
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
This paper presents an offering of some of the myriad connections between Combinatorics and Probability, directed in particular toward combinatorialists. The choice of material was dictated by the author's own interests, tastes and…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on…
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…
Probabilistic programs with dynamic computation graphs can define measures over sample spaces with unbounded dimensionality, which constitute programmatic analogues to Bayesian nonparametrics. Owing to the generality of this model class,…
Recently, B\'{e}nyi and the second author introduced two combinatorial interpretations for symmetrized poly-Bernoulli polynomials. In the present study, we construct bijections between these combinatorial objects. We also define various…
This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…
The article is an historical overview of some of the major contributions from different areas of Science with which, for centuries, it has been built up a scientific, sound and consistent vision of the atom. Some experiments that led us to…
We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is…