相关论文: Determining Covering Array Numbers via Balanced Co…
In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: 1. Some…
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather,…
We introduce and investigate binary $(k,k)$-designs -- combinatorial structures which are related to binary orthogonal arrays. We derive general linear programming bound and propose as a consequence a universal bound on the minimum possible…
Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this…
An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The overlap number of a graph is the minimum number of elements…
Connected Vertex Cover is one of the classical problems of computer science, already mentioned in the monograph of Garey and Johnson. Although the optimization and decision variants of finding connected vertex covers of minimum size or…
Motivated by representation theory we exhibit an interior structure to Catalan sequences and many generalisations thereof. Certain of these coincide with well known (but heretofore isolated) structures. The remainder are new.
Perfect codes are arguably the most fascinating structures in combinatorial coding theory, and their classification and weight distribution are of considerable interest. This classification also involves the analysis of some related…
We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then…
Some combinatorial designs, such as Hadamard matrices, have been extensively researched and are familiar to readers across the spectrum of Science and Engineering. They arise in diverse fields such as cryptography, communication theory, and…
We show that the class of conditional distributions satisfying the coarsening at Random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…
Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin. For online bin covering, competitive analysis fails…
We generate all the Orthogonal Arrays (OAs) of a given size n and strength t as the union of a collection of OAs which belong to an inclusion-minimal set of OAs. We derive a formula for computing the (Generalized) Word Length Pattern of a…
We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative…
We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer…
While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence…
We show that the class of conditional distributions satisfying the coarsening at random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…
The property of balance (in the sense of Feder and Mihail) is investigated in the context of paving matroids. The following examples are exhibited: (a) a class of ``sparse'' paving matroids that are balanced, but at the same time rich…
The generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion (Xu and Wu [Ann. Statist. 29 (2001) 1066-1077]). We provide a statistical…
Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinite towers of orbifolds uniformized by the complex 2-ball and some orbifolds over K3 surfaces uniformized by the 2-ball. Corresponding…