Let G be a connected, non-bipartite vertex-transitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product G×G are the preimages of the independent sets of maximal cardinality in G under projections, then the same holds for all finite tensor powers of G, thus providing an affirmative answer to a question raised by Larose and Tardif [8].

This article, a continuation of [HRo], constructs the Satake parameter for any irreducible smooth J-spherical representation of a p-adic group, where J is any parahoric subgroup. This parametrizes such representations when J is a special maximal parahoric subgroup. The main novelty is for groups which are not quasi-split, and the construction should play a role in formulating a geometric Satake...

Let s denote a compact convex object in IR. The f-width of s is the perpendicular distance between two distinct parallel lines of support of s with direction f . A set of disjoint convex compact objects in IR is of equal f -width if there exists a direction f such that every pair of objects have equal f -width. A visibility matching, for a set of equal f -width objects is a matching using non-c...

In this paper we define Sturmian graphs and we prove that all of them have a certain “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove t...

In this work we investigate infinite structures. We discuss the importance, meaning and temptation of the axiom of choice and equivalent formulations with respect to graph theory, abstract argumentation and dialogue games. Emphasis is put on maximal independent sets in graph theory as well as preferred semantics in abstract argumentation. 1998 ACM Subject Classification G.2.2 Graph Theory, F.4....

We associate a 2-complex to the following data: a presentation of a semigroup S and a transitive action of S on a set V by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex. A sufficient condition is given for the 2-complex to be simply connected. As a consequence we obtain simple topological proofs of results on presentations of Schüt...

A matching M of a graph G is maximal if it not proper subset any other in G. Maximal matchings are much less known and researched than their maximum perfect counterparts. In this paper we present the recurrences generating functions for sequences enumerating two classes chemically interesting linear polymers: polyspiro chains benzenoid chains. We also analyze asymptotic behavior those determine...

Abstract. Let Q be a first-order differential operator on a compact, smooth oriented Riemannian manifold with smooth boundary. Then, Friedrichs’ Extension Lemma states that the minimal closed extension Qmin (the closure of the graph) and the maximal closed extension Qmax (in the sense of distributions) of Q in L-spaces (1 ≤ p < ∞) coincide. In the present paper, we show that the same is true fo...

Let G = (S,E) be a plane straight line graph on a finite point set S ⊂ R in general position. For a point p ∈ S let the maximum incident angle of p in G be the maximum angle between any two edges of G that appear consecutively in the circular order of the edges incident to p. A plane straight line graph is called φopen if each vertex has an incident angle of size at least φ. In this paper we st...

For a set D of polyominoes, a packing of the plane with D is a maximal set of copies of polyominoes from D that are not overlapping. A packing with smallest density is called a clumsy packing. We give an example of a set D such that any clumsy packing is aperiodic. In addition, we compute the smallest possible density of a clumsy packing when D consists of a single polyomino of a given size and...