3 citations · 5 across the 5 of their papers we have counts for
6 papers
The Absolute Orders on the Coxeter Groups and are Sperner
Lawrence H. Harper, Gene B. Kim, Neal Livesay
Over 50 years ago, Rota posted the following celebrated `Research Problem': prove or disprove that the partial order of partitions on an -set (i.e., the refinement order) is Spe…
Is the Symmetric Group Sperner?
Larry H. Harper, Gene B. Kim
An antichain in a poset is a subset of in which no two elements are comparable. Sperner showed that the maximal antichain in the Boolean l…
The Edge-Isoperimetric Problem on Sierpinski Graphs: Final Resolution
L. H. Harper
This paper completes the project started in [10]; to solve the edge-isoperimetric problem on the (generalized and extended) Sierpinski graph, S(n,m). We prove that initial segments…
The edge-isorperimetric problem on Sierpinski graphs
L. H. Harper
Some families of graphs, such as the n-cubes and Sierpinski gaskets, are self-similar. In this paper we show how such recursive structure can be used systematically to prove isoper…
Can the Sierpinski graph be embedded in the Hamming graph?
Lawrence Hueston Harper
The (generalized & expanded) Sierpinski graph, S(n,m), and the Hamming graph have the same set of vertices (n-tuples from the set {0,1,...,m-1}. The edges of both are (unordered) p…
The Range of a Steiner Operation
L. H. Harper
This paper answers a fundamental question in the theory of Steiner operations (StOps) as defined and studied in the monograph, "Global Methods for Combinatorial Isoperimetric Probl…