Philippe Nadeau
About certain polynomials related to the Razumov--Stroganov conjecture.
Tue, 02/23/2010 - 16:01 — SomNambulAuthors: Philippe Nadeau, Tiago Fonseca
Subjects: Combinatorics
AbstractThe Razumov--Stroganov conjecture states that two families of numbers, both
indexed by noncrossing matchings of n points, are the same: on the one hand,
the number of Fully Packed Loop configurations on a grid with a given matching,
and on the other hand, the groundstate components in the O(1)--loop model. When
considering matchings with m nested arches, both families of numbers were shown
in previous works to be polynomial in m.Signed enumeration of ribbon tableaux.
Wed, 11/18/2009 - 16:01 — SomNambulAuthors: Philippe Nadeau, Dominique Gouyou-Beauchamps
Subjects: Combinatorics
AbstractWe give an extension of the classical Schensted correspondence to the case of
ribbon tableaux, where ribbons are allowed to be of different sizes. This is
done by extending Fomin's growth diagram approach of the classical
correspondence between permutations and pairs of standard tableaux of the same
shape, in particular by allowing signs in the enumeration. As an application we
give a combinatorial proof for the column sums of the character table of the
symmetric group.The structure of alternative tableaux.
Fri, 08/28/2009 - 23:56 — SomNambulAuthors: Philippe Nadeau
Subjects: Combinatorics
AbstractIn this paper we study alternative tableaux introduced by Viennot. These
tableaux are in simple bijection with permutation tableaux, defined previously
by Postnikov . We exhibit a simple recursive structure for alternative
tableaux. From this decomposition, we can easily deduce a number of enumerative
results. We also give bijections between these tableaux and certain classes of
labeled trees. Finally, we exhibit a bijection with permutations, and relate it
to some other bijections that already appeared in the literature.
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