Related papers: Flip Graphs for Polynomial Multiplication
In this paper, we study the flip graph on the perfect matchings of a complete graph of even order. We investigate its combinatorial and spectral properties including connections to the signed reversal graph and we improve a previous upper…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal…
Flip graphs are a ubiquitous class of graphs, which encode relations induced on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance, are the graphs induced by quadrilateral flips in…
We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
This document is a companion for the Maple program \textbf{Summing a polynomial function over integral points of a polygon}. It contains two parts. First, we see what this programs does. In the second part, we briefly recall the…
There are two kinds of polynomial functions on matrix algebras over commutative rings: those induced by polynomials with coefficients in the algebra itself and those induced by polynomials with scalar coefficients. In the case of algebras…
By using the Poisson formula for resultants and the variants of chip-firing game on graphs, we provide a combinatorial method for computing a class of of resultants, i.e. the characteristic polynomials of the adjacency tensors of starlike…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously…
We describe a general algorithm for generating various families of ribbon tableaux and computing their spin polynomials. This algorithm is derived from a new matricial coding. An advantage of this new notation lies in the fact that it…
We consider the flip-width of geometric graphs, a notion of graph width recently introduced by Toru\'nczyk. We prove that many different types of geometric graphs have unbounded flip-width. These include interval graphs, permutation graphs,…
Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
Flip graphs of combinatorial and geometric objects are at the heart of many deep structural insights and connections between different branches of discrete mathematics and computer science. They also provide a natural framework for the…
In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial…
It is suggested to use multi-layer graphs as a mathematical model in the design of MPLS networks. The application of this model makes it possible to design multi-service telecommunication systems simultaneously at several levels and to…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In…