2,539 research outputs found
Algorithms for Longest Common Abelian Factors
In this paper we consider the problem of computing the longest common abelian
factor (LCAF) between two given strings. We present a simple
time algorithm, where is the length of the strings and is the
alphabet size, and a sub-quadratic running time solution for the binary string
case, both having linear space requirement. Furthermore, we present a modified
algorithm applying some interesting tricks and experimentally show that the
resulting algorithm runs faster.Comment: 13 pages, 4 figure
Van der Waerden's Theorem and Avoidability in Words
Pirillo and Varricchio, and independently, Halbeisen and Hungerbuhler
considered the following problem, open since 1994: Does there exist an infinite
word w over a finite subset of Z such that w contains no two consecutive blocks
of the same length and sum? We consider some variations on this problem in the
light of van der Waerden's theorem on arithmetic progressions.Comment: Co-author added; new result
A Note on Easy and Efficient Computation of Full Abelian Periods of a Word
Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced
the idea of an Abelian period with head and tail of a finite word. An Abelian
period is called full if both the head and the tail are empty. We present a
simple and easy-to-implement -time algorithm for computing all
the full Abelian periods of a word of length over a constant-size alphabet.
Experiments show that our algorithm significantly outperforms the
algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the
same problem.Comment: Accepted for publication in Discrete Applied Mathematic
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
Categorification of (induced) cell modules and the rough structure of generalized Verma modules
This paper presents categorifications of (right) cell modules and induced
cell modules for Hecke algebras of finite Weyl groups. In type we show that
these categorifications depend only on the isomorphism class of the cell
module, not on the cell itself. Our main application is multiplicity formulas
for parabolically induced modules over a reductive Lie algebra of type ,
which finally determines the so-called rough structure of generalized Verma
modules. On the way we present several categorification results and give the
positive answer to Kostant's problem from \cite{Jo} in many cases. We also give
a general setup of decategorification, precategorification and
categorification.Comment: 59 page
- …