52 research outputs found
On the topology of two partition posets with forbidden block sizes
AbstractWe study two subposets of the partition lattice obtained by restricting block sizes. The first consists of set partitions of {1,ā¦,n} with block size at most k, for kā¤nā2. We show that the order complex has the homotopy type of a wedge of spheres, in the cases 2k+2ā„n and n=3k+2. For 2k+2>n, the posets in fact have the same Snā1-homotopy type as the order complex of Ī nā1, and the Sn-homology representation is the ātree representationā of Robinson and Whitehouse. We present similar results for the subposet of Ī n in which a unique block size kā„3 is forbidden. For 2kā„n, the order complex has the homotopy type of a wedge of (nā4)-spheres. The homology representation of Sn can be simply described in terms of the Whitehouse lifting of the homology representation of Ī nā1
A q-analog of the Seidel generation of Genocchi numbers
A new -analog of Genocchi numbers is introduced through a q-analog of
Seidel's triangle associated to Genocchi numbers. It is then shown that these
-Genocchi numbers have interesting combinatorial interpretations in the
classical models for Genocchi numbers such as alternating pistols, alternating
permutations, non intersecting lattice paths and skew Young tableaux.Comment: 17 page
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