Related papers: Numerical Algorithm for P\'olya Enumeration Theore…
We describe an algorithm that computes the index of a finitely generated subgroup in a finitely $L$-presented group provided that this index is finite. This algorithm shows that the subgroup membership problem for finite index subgroups in…
Vizing's theorem guarantees that every graph with maximum degree $\Delta$ admits an edge coloring using $\Delta + 1$ colors. In online settings - where edges arrive one at a time and must be colored immediately - a simple greedy algorithm…
Generative molecular design has moved from proof-of-concept to real-world applicability, as marked by the surge in very recent papers reporting experimental validation. Key challenges in explainability and sample efficiency present…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number is the smallest number k such that G admits such equitable k-coloring. We focus…
In this paper we consider the following question in the spirit of Ramsey theory: Given $x\in A^\omega,$ where $A$ is a finite non-empty set, does there exist a finite coloring of the non-empty factors of $x$ with the property that no…
Chromatic polynomials are important objects in graph theory and statistical physics, but as a result of computational difficulties, their study is limited to graphs that are small, highly structured, or very sparse. We have devised and…
The Estimation of Distribution Algorithm is a new class of population based search methods in that a probabilistic model of individuals is estimated based on the high quality individuals and used to generate the new individuals. In this…
We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
This article demonstrates, using numerous examples of varying complexity, how one can visually prove summation formulas involving binomial coefficients by exclusively using the recurrence relation for binomial coefficients and its…
A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…
We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…
A problem based on the Extended Euclidean Algorithm applied to a class of polynomials with many factors is presented and believed to be hard. If so, it is a one-way function well suited for applications in digital signicatures.
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
An algorithm counting the number of ones in a binary word is presented running in time $O(\log\log b)$ where $b$ is the number of ones. The operations available include bit-wise logical operations and multiplication.
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…
The method of Hol\'y, Sokol and \v{C}ern\'y (Applied Soft Computing, 2017, Vol. 60, p. 752-762) clusters objects based on their incidence in a large number of given sets. The idea is to minimize the occurrence of multiple objects from the…