Related papers: The area generating function for simple-2-column p…
For a positive integer $n\geq 3$, the sides and diagonals of a convex $n$-gon divide the interior of the convex $n$-gon into finitely (polynomial in $n$) many regions bounded by them. In this article, we associate to every region a unique…
A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization and a corresponding package…
We present a simplified formulation of open intersection numbers, as an alternative to the theory initiated by Pandharipande, Solomon and Tessler. The relevant moduli spaces consist of Riemann surfaces (either with or without boundary) with…
Punctured polygons are polygons with internal holes which are also polygons. The external and internal polygons are of the same type, and they are mutually as well as self-avoiding. Based on an assumption about the limiting area…
We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…
We investigate a generalization of stacks that we call $\mathcal{C}$-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that $\mathcal{C}$-machines generate, and how these systems of…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be…
Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given. By applying this generating function, not only derivative of these polynomials but also…
We consider the tiling generating functions of semi-hexagons and quartered hexagons with dents on their sides. In general, there are no simple product formulas for these generating functions. However, we show that the modification in the…
In this paper, we consider the problem of covering a plane region with unit discs. We present an improved upper bound and the first nontrivial lower bound on the number of discs needed for such a covering, depending on the area and…
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…
We construct a generating functional for the exact evalutation of a coherent representation of spin network amplitudes. This generating functional is defined for arbitrary graphs and depends only on a pair of spinors for each edge. The…
We consider Problem 6.94 posed in the book Concrete Mathematics by Graham, Knuth, and Patashnik, and solve it by using bivariate exponential generating functions. The family of recurrence relations considered in the problem contains many…
Fibonacci polynomials are generalizations of Fibonacci numbers, so it is natural to consider polynomial versions of the various results for Fibonacci numbers. According to Hong, Pongsriiam, Bulawa, and Lee, the generating function of the…
Polyominoes have been the focus of many recreational and research investigations. In this article, the authors investigate whether a paper cutout of a polyomino can be folded to produce a second polyomino in the same shape as the original,…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
Dealing with large numbers of symmetries is often problematic. One solution is to focus on just symmetries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete,…
We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column)…
In this paper, we present some criteria for the $2$-$q$-log-convexity and $3$-$q$-log-convexity of combinatorial sequences, which can be regarded as the first column of certain infinite triangular array $[A_{n,k}(q)]_{n,k\geq0}$ of…
Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating…