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We consider partitions of a set with r elements ordered by refinement. We consider the simplicial complex Kˉ(r) formed by chains of partitions which starts at the smallest element and ends at the larg...
Soil in alpine environments plays a key role in the development of ecosystem services and in order to maintain and preserve this important resource, information is required on processes that lead to s...
Motivated by the structure of the uniform posets we introduce the notion of an augmented down-up (or ADU) algebra. We discuss how ADU algebras are related to the down-up algebras defined by Benkart an...
Abstract: A geometric graph G(bar) is a simple graph drawn in the plane, on points in general position, with straight-line edges. We call G(bar) a geometric realization of the underlying abstract grap...
Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where ...
The Rees product of posets      Rees product  posets        2010/12/10
We determine how the flag f-vector of any graded poset changes under the Rees product with the chain, and more generally, any t-ary tree. As a corollary, the M¨obius function of the Rees product of a...
Level Eulerian Posets      Level Eulerian Posets        2010/12/8
The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecompos...
Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ fo...

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