In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the performance of...
In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer alge...
In this paper we give combinatorial proofs of some well known identities and obtain some generalizations. We give a visual proof of a result of Chapman and Costas-Santos regarding the determinant of sum of matrices. Also we find a new identity expres...
In this study we revisit the telephone exchange problem. We discuss a generalization of the telephone exchange problem by discuss two generalizations of the Bessel polynomials. We study combinatorial properties of these polynomials, and show how the...
The cave polynomial of a polymatroid was recently introduced and used to study the syzygies of polymatroidal ideals. We study the combinatorial relationships between three formulas for the cave polynomial. As an application, we interpret the Snapper...
Preventing poaching through ranger patrols protects endangered wildlife, directly contributing to the UN Sustainable Development Goal 15 of life on land. Combinatorial bandits have been used to allocate limited patrol resources, but existing approach...
The main goal of this paper is to assign two combinatorial interpretations to the elements of the Rascal Triangle defined by Angorro et al. The first interpretation involves counting ascents in binary words, while the second interpretation involves p...
Combinatorial transgressions are secondary invariants of a space admitting triangulations. They arise from subdivisions and are analogous to transgressive forms such as those arising in Chern-Weil theory. Unlike combinatorial characteristic classes...
We develop a finite-state automata approach, implemented in a Maple package {\tt ToadsAndFrogs} available from our websites, for conjecturing, and then rigorously proving, values for large families of positions in Richard Guy's combinatorial game `...
Let $(X, d)$ be a semimetric space. A permutation $Φ$ of the set $X$ is a combinatorial self similarity of $(X, d)$ if there is a bijective function $f \colon d(X^2) \to d(X^2)$ such that $$ d(x, y) = f(d(Φ(x), Φ(y))) $$ for all $x$, $y \in X$. We...
The group of combinatorial self-similarities of a pseudometric space $(X, d)$ is the maximal subgroup of the symmetric group $\mathbf{Sym} (X)$ whose elements preserve the four-point equality $d(x,y)=d(u,v)$. Let us denote by $\mathcal{IP}$ the class...
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions containing n...
This paper brings an in detail Genetic Algorithm (GA) based combinatorial optimization method used for the optimal design of the water distribution network (WDN) of Gurudeniya Service Zone, Sri Lanka. Genetic Algorithm (GA) mimics the survival of the...
A barcode is a finite multiset of intervals on the real line. Jaramillo-Rodriguez (2023) previously defined a map from the space of barcodes with a fixed number of bars to a set of multipermutations, which presented new combinatorial invariants on th...
Cassidy, Phan and Shelton associate to any regular cell complex X a quadratic K-algebra R(X). They give a combinatorial solution to the question of when this algebra is Koszul. The algebra R(X) is a combinatorial invariant but not a topological inv...
This article is a sequel to a recent article by Eric Rowland and Reem Yassawi, presenting yet another approach to the fast determination of congruence properties of `famous' combinatorial sequences. The present approach can be taught to a computer, a...
In this work, we give combinatorial proofs for generating functions of two problems, i.e., flushed partitions and concave compositions of even length. We also give combinatorial interpretation of one problem posed by Sylvester involving flushed parti...
One way to study certain classes of polynomials is by considering examples that are attached to combinatorial objects. Any graph $G$ has an associated reciprocal polynomial $R_G$, and with two particular classes of reciprocal polynomials in mind one...
We study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals. While the packing problem is currently unresolved, we successfully settle the validity of i...
The Multiple Depot Ring-Star Problem (MDRSP) is an important combinatorial optimization problem that arises in the context of optical fiber network design, and in applications pertaining to collecting data using stationary sensing devices and autonom...