Related papers: Combinatorial Reciprocity Theorems
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: 1. Some…
Combinatorial $t$-designs have been an interesting topic in combinatorics for decades. It was recently reported that the image sets of a fixed size of certain special polynomials may constitute a $t$-design. Till now only a small amount of…
We present a unified framework of combinatorial descriptions, and the analogous asymptotic growth of the coefficients of two general families of functions related to integer partitions. In particular, we resolve several conjectures and…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
The goal of this note is to present a combinatorial mechanism for counting certain objects associated to a variety X defined over a finite field. The basic example is that of counting conjugacy classes in GL_n(F_q), where X is the…
In this article we tackle the combinatorics of coloured hard-dimer objects. This is achieved by identifying coloured hard-dimer configurations with a certain class of rooted trees that allow for an algebraic treatment in terms of…
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
We introduce poly-Cauchy permutations that are enumerated by the poly-Cauchy numbers. We provide combinatorial proofs for several identities involving poly-Cauchy numbers and some of their generalizations. The aim of this work is to…
We establish a connection between root multiplicities for Borcherds-Kac-Moody algebras and graph coloring. We show that the generalized chromatic polynomial of the graph associated to a given Borcherds algebra can be used to give a closed…
In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which…