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Enumerative Combinatorics focusses on the exact and asymptotic counting of combinatorial objects. It is strongly connected to the probabilistic analysis of large combinatorial structures and has fruitful connections to several disciplines, including statistical physics, algebraic combinatorics, graph theory and computer science. This workshop brought together experts from all these various fiel...

Enumeration, alias counting, is the oldest mathematical subject, while Algebraic Combinatorics is one of the youngest. Some cynics claim that Algebraic Combinatorics is not really a new subject but just a new name given to Enumerative Combinatorics in order to enhance its (former) poor image, but Algebraic Combinatorics is in fact the synthesis of two opposing trends: abstraction of the concret...

Abstract We initiate the study of enumerative combinatorics intervals in Dyck pattern poset. More specifically, we find some closed formulas to express size specific intervals, as well number their covering relations. In most cases, are also able refine our by rank. provide first results on Möbius function poset, giving for instance a expression initial whose maximum is path having exactly two ...

We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of the Eulerian polynomials, the one in symmetric function theory deals with a refinement of the chromatic symmetric functions of Stanley, and the one in algebra...

In this section we will discuss the Inclusion-Exclusion principle, with a few applications (including a formula for the chromatic polynomial of a graph), and then consider a wide generalisation of it due to Gian-Carlo Rota, involving the Möbius function of a partially ordered set. The q-binomial theorem gives a simple formula for the Möbius function of the lattice of subspaces of a vector space.

Problems of enumerative combinatorics are solved for the proposed scheme, i. e. number its outcomes is determined, their direct listing constructed, numbering problem solved, probability distribution scheme found, and a procedure modeling proposed.

One of the draws of combinatorics is its ability to take inspiration from, motivate, and even push forward diverse areas of mathematics and computer science. In particular, much current research focuses on the use of analytic techniques to address questions of computability and complexity in enumerative combinatorics. The universality of many analytic statements often allows for very general en...

The combinatorial theory of species developed by Joyal provides a foundation for enumerative combinatorics of objects constructed from finite sets. In this paper we develop an analogous theory for the enumerative combinatorics of objects constructed from vector spaces over finite fields. Examples of these objects include subspaces, flags of subspaces, direct sum decompositions, and linear maps ...