On the Parikh-de-Bruijn grid

We introduce the Parikh-de-Bruijn grid, a graph whose vertices are fixed-order Parikh vectors, and whose edges are given by a simple shift operation. This graph gives structural insight into the nature of sets of Parikh vectors as well as that of the Parikh set of a given string. We show its utility by proving some results on Parikh-de-Bruijn strings, the abelian analog of de-Bruijn sequences.Comment: 18 pages, 3 figures, 1 tabl

28th Annual Symposium on Combinatorial Pattern Matching : CPM 2017, July 4-6, 2017, Warsaw, Poland

Peer reviewe

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Characters of (relatively) integrable modules over affine Lie superalgebras

In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules L over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras g. The problem consists of two parts. First, it is the reduction of the problem to the [bar over g]-module F(L), where [bar over g] is the associated to L integral Lie superalgebra and F(L) is an integrable irreducible highest weight [bar over g]-module. Second, it is the computation of characters of integrable highest weight modules. There is a general conjecture concerning the first part, which we check in many cases. As for the second part, we prove in many cases the KW-character formula, provided that the KW-condition holds, including almost all finite-dimensional g-modules when g is basic, and all maximally atypical non-critical integrable g-modules when g is affine with non-zero dual Coxeter number.Simons Foundation. Postdoctoral Fellowshi

Bridges from Lattice QCD to Nuclear Physics

A review is given of attempts to bridge the gap between everyday particle and nuclear physics - involving many quarks - and the basic underlying theory of QCD that can only be evaluated exactly for few quark systems. Even the latter requires the original theory of QCD to be discretised to give Lattice QCD - but this modification can still yield exact results for the original theory. These LQCD results can then be considered on a similar footing to experimental data - namely as cornerstones that must be fitted by phenomenological models. In this way, the hope is that "QCD inspired" models can become more and more "QCD based" models, by fixing - in the few-quark case where LQCD can be carried out - the form of these models in such a way that they can be extended to multi-quark systems.Comment: 118 pages, 25 figures. A chapter in Volume 9 of International Review of Nuclear Physics, "Hadronic Physics from Lattice QCD", (Ed. A. M. Green, World Scientific