The peak set of a permutation Ïƒ is the set {i : Ïƒ (i âˆ’ 1) < Ïƒ (i) > Ïƒ (i + 1)}. The group algebra of the symmetric group Sn admits a subalgebra in which elements are sums of permutations with aâ€¦ (More)

We introduce a generalized cake-cutting problem inwhichwe seek to divide multiple cakes so that two players may get their mostpreferred piece selections: a choice of one piece from each cake,â€¦ (More)

We show that Fanâ€™s 1952 lemma on labelled triangulations of the n-sphere with n + 1 labels is equivalent to the Borsukâ€“Ulam theorem. Moreover, unlike other Borsukâ€“Ulam equivalents, we show that thisâ€¦ (More)

We study degree sequences for simplicial posets and polyhedral complexes, generalizing the well-studied graphical degree sequences. Here we extend the more common generalization of vertex-to-facetâ€¦ (More)

We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake,â€¦ (More)

The flag Whitney numbers (also referred to as the flag f -numbers) of a geometric lattice count the number of chains of the lattice with elements having specified ranks. We give a collection ofâ€¦ (More)

In this paper we extend the work of Bogart and Trenk [3] and Fishburn and Trotter [6] in studying different classes of bitolerance orders. We provide a more comprehensive list of classes ofâ€¦ (More)