Related papers: Combinatorial theorems relative to a random set
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
In this paper we present several natural $q$-analogues of the poly-Bernoulli numbers arising in combinatorial contexts. We also recall some relating analytical results and ask for combinatorial interpretations.
This article is an exposition of recent results on self-similar sets, asserting that if the dimension is smaller than the trivial upper bound then there are almost overlaps between cylinders. We give a heuristic derivation of the theorem…
Analogues of Kolmogorov comparison theorems and some of their applications were established.
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
A fascinating conjectural connection between statistical mechanics and combinatorics has in the past five years led to the publication of a number of papers in various areas, including stochastic processes, solvable lattice models and…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for…
Comparative prime number theory is the study of the {\em{discrepancies}} of distributions when we compare the number of primes in different residue classes. This work presents a list of the problems being investigated in comparative prime…
I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
We present a relative form of the Toponogov comparison theorem.
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…
We retrace the recent history of the Umbral Calculus. After studying the classic results concerning polynomial sequences of binomial type, we generalize to a certain type of logarithmic series. Finally, we demonstrate numerous typical…
The paper presents several combinatorial properties of the boolean cumulants. A corollary is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted for the case of boolean independence with…