8 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…
Fibonacci and Catalan Numbers Meet in Staircase Polyominoes
Jean-Luc Baril, José Luis RamÃrez, Samuel RamÃrez +1
We study Fibonacci (staircase) polyominoes, a class of column-convex polyominoes whose lower boundary is a staircase with unit vertical steps. We derive multivariate generating fun…
Enumerations and Bijections for Stanley Polyominoes
Jean-Luc Baril, Aubrey Blecher, José Luis ramÃrez
Stanley polyominoes are a subclass of parallelogram polyominoes in which each row begins strictly to the right of the beginning of the previous row and ends strictly to the right o…
Black Cell Capacity in Catalan polyominoes
Jean-Luc Baril, Sela Fried, Nathanaël Hassler +1
A Catalan word is a sequence of nonnegative integers such that and for . Given a Catalan word, we construct a column…
Enumeration of paths in a hexagonal circle packing
Jean-Luc Baril, José Luis Ramà rez
We investigate paths in the hexagonal circle packing and enumerate them with respect to width, height, number of steps, area, and kissing number. Functional equations and the kerne…
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…