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5 papers · 2 filters
A bijective proof of an unusual symmetric group generating function
Mike Zabrocki
For , let denote the descent set of . The length of the permutation is the number of inversions, denoted by $inv(σ) = \big | \{(i,j) :…
Combinatorial Hopf algebras and generalized Dehn-Sommerville relations
Marcelo Aguiar, Nantel Bergeron, Frank Sottile
A combinatorial Hopf algebra is a graded connected Hopf algebra over a field equipped with a character (multiplicative linear functional) . We show that the terminal…
Planar Minimally Rigid Graphs and Pseudo-Triangulations
Ruth Haas, David Orden, Guenter Rote +6
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than 180 degrees. In this paper we prove th…
The peak algebra and the Hecke-Clifford algebras at
Nantel Bergeron, Florent Hivert, Jean-Yves Thibon
Using the formalism of noncommutative symmetric functions, we derive the basic theory of the peak algebra of symmetric groups and of its graded Hopf dual. Our main result is to pro…
The peak algebra and the descent algebras of types B and D
Marcelo Aguiar, Nantel Bergeron, Kathryn Nyman
We show the existence of a unital subalgebra of the symmetric group algebra linearly spanned by sums of permutations with a common peak set, which we call the peak algebra. We show…