1 citations · 1 across the 8 of their papers we have counts for
9 papers
(Un)ranking Permutation Classes
Nathanaël Hassler, Vincent Vajnovszki
Permutations avoiding a pattern of length three are enumerated by the Catalan numbers. In this work, we present methods for ranking and unranking such permutations in lexicographic…
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…
A bijection between edges of the Turán graph and irreducible elements in the dominance order lattice
Nathanaël Hassler
In this paper we build a bijection between the meet-irreducible elements of the lattice of the compositions of with parts in equipped with the dominance order, and the…
Emerging consecutive pattern avoidance
Nathanaël Hassler, Sergey Kirgizov
In this note we study the asymptotic popularity, that is, the limit probability to find a given consecutive pattern at a random position in a random permutation in the eighteen cla…
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…
Notes on sum-free sets in abelian groups
Nathanaël Hassler, Andrew Treglown
In this paper we highlight a few open problems concerning maximal sum-free sets in abelian groups. In addition, for most even order abelian groups we asymptotically determine t…
Intervals in a family of Fibonacci lattices
Jean-Luc Baril, Nathanaël Hassler
We focus on a family of subsets $(\F^p_n)_{p\geq 2}$ of Dyck paths of semilength that avoid the patterns and , which are enumerated by the generalized Fibonacci…
Greedy Gray Codes for some Restricted Classes of Binary Words
Nathanaël Hassler, Vincent Vajnovszki, Dennis Wong
We investigate the existence of greedy Gray codes, based on the choice of the first element in the code, for two classes of binary words: generalized Fibonacci words and generalize…
On maximal sum-free sets in abelian groups
Nathanaël Hassler, Andrew Treglown
Balogh, Liu, Sharifzadeh and Treglown [Journal of the European Mathematical Society, 2018] recently gave a sharp count on the number of maximal sum-free subsets of $\{1, \dots, n\}…