In the last couple of years many research papers have been devoted to Abelian complexity of words. Recently, Constantinescu and Ilie (Bulletin EATCS 89, 167–170, 2006) introduced the notion of Abelian period. In this article we present two quadratic brute force algorithms for computing Abelian periods for special cases and a quasi-linear algorithm for computing all the Abelian periods of a word.

We present a construction of an entropy-preserving equivariant surjective map from the d-dimensional critical sandpile model to a certain closed, shift-invariant subgroup of T d (the ‘harmonic model’). A similar map is constructed for the dissipative abelian sandpile model and is used to prove uniqueness and the Bernoulli property of the measure of maximal entropy for that model.

The Jacobian of a graph, also known as the Picard Group, Sandpile Group, or Critical Group, is a discrete analogue of the Jacobian of an algebraic curve. It is known that the order of the Jacobian of a graph is equal to its number of spanning trees, but the exact structure is known for only a few classes of graphs. In this paper, we compute the Jacobian for graphs of the form Kn\E(H) where H is...

In this paper we derive the scaling fields in c = −2 conformal field theory associated with weakly allowed clusters in abelian sandpile model and show a direct relation between the two models.

Our aim is to introduce and study a new partial integrodifferential equation (PIDE) associated with the dynamics of some physical granular structure with arbitrary component sizes, like a sandpile or sea dyke. Our PIDE is closely related to the nonlocal evolution problem introduced in [F. Andreu et al., Calc. Var. Partial Differential Equations, 35 (2009), pp. 279–316] by studying the limit, as...

Let Tn be a (d − 1)-ary tree of height n. A bilateral regular tree is the multigraph T d n,n that is defined by : (i) juxtaposing two Tn’s, (ii) drawing a new edge between two roots and (iii) drawing d− 1 edges between each leaf and a new vertex, called the sink. In this paper the sandpile group of T d n,n is determined.

Adding grains at a single site on a flat substrate in the abelian sandpile models produces beautiful complex patterns. We study in detail the pattern produced by adding grains on a two-dimensional square lattice with directed edges (each site has two arrows directed inward and two outward), starting with a periodic background with half the sites occupied. The model shows proportionate growth an...

The QCD infrared dynamics appears to be well approximated by a (dual) Abelian Higgs model [1,2]. Via Abelian projection the QCD gluodynamics is reduced to Abelian elds, Abelian monopoles and charged matter elds degrees of freedom. Then, lattice simulations (mainly in SU(2) and in Maximal Abelian projection) show Abelian dominance and monopole dominance in the long range features of QCD. This me...

The QCD infrared dynamics appears to be well approximated by a (dual) Abelian Higgs model [1,2]. Via Abelian projection the QCD gluodynamics is reduced to Abelian fields, Abelian monopoles and charged matter fields degrees of freedom. Then, lattice simulations (mainly in SU(2) and in Maximal Abelian projection) show Abelian dominance and monopole dominance in the long range features of QCD. Thi...

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...