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- California Institute of TechnologyUS17 papers
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4 papers · 2 filters
A combinatorial proof of the Rogers-Ramanujan and Schur identities
Cilanne Boulet, Igor Pak
We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direct bij…
The Positive Bergman Complex of an Oriented Matroid
Federico Ardila, Caroline Klivans, Lauren Williams
We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive B…
Inequalities for the h- and flag h-vectors of geometric lattices
Kathryn Nyman, Ed Swartz
We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if D(L) is the order complex of a rank (r+1) geometric lattice L, then for…
Irreducible compositions and the first return to the origin of a random walk
Edward A. Bender, Gregory F. Lawler, Robin Pemantle +1
Let be a pair of compositions of into positive parts. We say this pair is {\em irreducible} if there is no positive for…