Kathryn L. Nyman

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The peak set of a permutation σ is the set {i : σ (i − 1) < σ (i) > σ (i + 1)}. The group algebra of the symmetric group Sn admits a subalgebra in which elements are sums of permutations with a common descent set. In this paper we show the existence of a subalgebra of this descent algebra in which elements are sums of permutations sharing a common peak set.(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 of bitolerance orders and prove equality between some of these classes in general and other classes in the bipartite domain. We also provide separating examples between(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, allowing for the possibility of linked preferences over the cakes. For two players, we show that disjoint envy-free piece selections may not exist for two cakes cut(More)
The peak algebra P n is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks. By exploiting the combinatorics of sparse subsets of [n− 1] (and of certain classes of compositions of n called almost-odd and thin), we construct three new linear bases of P n. We discuss two peak analogs of the(More)
We consider an extension of the 2-person Rényi-Ulam liar game in which lies are governed by a channel C, a set of allowable lie strings of maximum length k. Carole selects x ∈ [n], and Paul makes t-ary queries to uniquely determine x. In each of q rounds, Paul weakly partitions [n] = A 0 ∪· · ·∪A t−1 and asks for a such that x ∈ A a. Carole responds with(More)
We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if ∆(L) is the order complex of a rank (r + 1) geometric lattice L, then the for all i ≤ r/2 the h-vector of ∆(L) satisfies, h i−1 ≤ h i and h i ≤ h r−i. We also obtain several inequalities for the flag h-vector of ∆(L) by analyzing the weak Bruhat order(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 of inequalities which imply all the linear inequalities satisfied by the flag Whitney numbers of rank 3 geometric lattices. We further describe the smallest closed(More)
A Borsuk-Ulam equivalent that implies Sperner's Lemma. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR,(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-facet degree sequences by considering arbitrary face-to-flag degree sequences. In particular, these may be viewed as natural refinements of the flag f-vector of the(More)