Related papers: Friendship theorem: A combinatorial proof

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…

In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.

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…

The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary…

In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…

A paper of the first author and Zilke proposed seven combinatorial problems around formulas for the characteristic polynomial and the exponents of an isolated quasihomogeneous singularity. The most important of them was a conjecture on the…

We prove Terao conjecture saying that the freeness is determined by the combinatorics for arrangements of 13 lines in the complex projective plane and that the property of being nearly free is combinatorial for line arrangements of up to 12…

We consider a combinatorial problem occurring naturally in a group theoretical setting and provide a constructive solution in a special case. More precisely, in 1999 the author established a logarithmic bound for the derived length of the…

We consider the generalised friendship paradox, focussing on the number of triangles at a vertex as the relevant attribute. We show that, contrary to the setting where the attribute is the number of edges at a vertex or the number of wedges…

An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.

The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…

An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…

Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three…

We present a powerful theorem for proving the irreducibility of tempered unitary representations of the free group.

We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…

We introduce a one-person game that we call Padlock Solitaire which resembles the well-known clock solitaire card game. Analyzing variants of this game we obtain simple proofs of some classical results of combinatorics including ballot…

The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…

We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…

The famous contradiction of a bijection between a set and its power set is a consequence of the impredicative definition involved. This is shown by the fact that a simple mapping between equivalent sets does also fail to satisfy the…

The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…