7 papers
Enumeration in the lattice of -decreasing words
Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov
We prove that the poset of -decreasing words equipped with the componentwise order forms a lattice. We enumerate the join-irreducible elements for arbitrary , and for any p…
Brick Wall Excursions: Combinatorial Interpretation of Random Flight Moments
Sergey Kirgizov, Khaydar Nurligareev, Michael Wallner
We study the expected distance of short uniform random walks in arbitrary dimensions with unit steps in random directions. It is known that for dimensions and , all the…
Emerging consecutive pattern avoidance
Nathanaël Hassler, Sergey Kirgizov
In this note we study the {\em asymptotic popularity}, that is, the limit probability to find a given consecutive pattern at a random position in a random permutation in the eighte…
The ascent lattice on Dyck paths
Jean-Luc Baril, Mireille Bousquet-Mélou, Sergey Kirgizov +1
In the Stanley lattice defined on Dyck paths of size , cover relations are obtained by replacing a valley by a peak . We investigate a greedy version of this lattice, f…
A lattice on Dyck paths close to the Tamari lattice
Jean-Luc Baril, Sergey Kirgizov, Mehdi Naima
We introduce a new poset structure on Dyck paths where the covering relation is a particular case of the relation inducing the Tamari lattice. We prove that the transitive closure…
Grand zigzag knight's paths
Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov +1
We study the enumeration of different classes of grand knight's paths in the plane. In particular, we focus on the subsets of zigzag knight's paths that are subject to constraints.…