Nathanaël est doctorant au LIB, dans l’équipe Combinatoire-Réseaux.
Titre : Enumeration in the lattice of q-decreasing words.
Résumé : A binary word is called q-decreasing, for q > 0, if inside this word each of length-maximal (in the local sense) occurrences of a factor of the form 0^a1^b, a > 0, satisfies q·a > b. We prove that the poset of q-decreasing words equipped with the componentwise order forms a lattice. We enumerate the join-irreducible elements for arbitrary q > 0, and for any positive rational number q, we determine the number of coverings, intervals and meet-irreducible elements. The latter present the same structure as words over an alphabet of 2⌈q⌉ + 1 letters avoiding ⌈q⌉^2 + 2⌈q⌉ − 1 consecutive patterns of length 2.
Site web : https://perso.eleves.ens-rennes.fr/people/nathanael.hassler/