Related papers: Closed-form expansions for the universal edge elim…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
In this work, considering a general subclass of bi-univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
The concept of a composed product for univariate polynomials has been explored extensively by Brawley, Brown, Carlitz, Gao, Mills, et al. Starting with these fundamental ideas and utilizing fractional power series representation (in…
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
In this paper, we first present combinatorial proofs of a kind of expansions of the Eulerian polynomials of types A and B, and then we introduce Stirling permutations of the second kind. In particular, we count Stirling permutations of the…
By polynomial (or extended binomial) coefficients, we mean the coefficients in the expansion of integral powers, positive and negative, of the polynomial $1+t +\cdots +t^{m}$; $m\geq 1$ being a fixed integer. We will establish several…
We study powers of binomial edge ideals associated with closed and block graphs.
Our goal in this work is to found a closed form for rational generat- ing functions, these generate a various families of polynomials and generalized polynomials, in order to get the general recursive formula satisfied by these polynomials.
In this article, we obtain quasiconformal extensions of some classes of conformal maps defined either on the unit disc or on the exterior of it onto the extended complex plane. Some of these extensions have been obtained by constructing…
In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series…
We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and colored permutations. The corresponding…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded…
We compute an analogue of Pascal's triangle enriched in bilinear forms over a finite field. This gives an arithmetically meaningful count of the ways to choose $j$ ring homomorphisms into an algebraic closure from an \'etale extension of…
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.
In this paper, we give a reduced formula of the characteristic polynomial of $k$-uniform hypergraphs with a pendant edge. And the explicit characteristic polynomial and all distinct eigenvalues of $k$-uniform hyperpath are given.