Serial digital decoder Patent

Serial digital decoder design with square circuit matrix and serial memory storage unit

Concept for simplified serial digital decoder

Modular decoder, which lends itself best to special purpose digital equipment using sequential access memories, decodes the first order Reed-Muller codes. It functions as a maximum-likelihood exhaustive-search decoder and is a modular implementation to accommodate codes of any length

Layout tool Patent

Design and development of layout tool for machine shop use to locate point in precise reference to straight or bowed reference edg

Homology representations arising from the half cube, II

In a previous work (arXiv:0806.1503v2), we defined a family of subcomplexes of the $n$-dimensional half cube by removing the interiors of all half cube shaped faces of dimension at least $k$, and we proved that the homology of such a subcomplex is concentrated in degree $k-1$. This homology group supports a natural action of the Coxeter group $W(D_n)$ of type $D$. In this paper, we explicitly determine the characters (over ${\Bbb C}$) of these homology representations, which turn out to be multiplicity free. Regarded as representations of the symmetric group $S_n$ by restriction, the homology representations turn out to be direct sums of certain representations induced from parabolic subgroups. The latter representations of \sym_n agree (over ${\Bbb C}$) with the representations of \sym_n on the $(k-2)$-nd homology of the complement of the $k$-equal real hyperplane arrangement.Comment: 19 pages AMSTeX. One figure. The Conjecture in the previous version is now a Theorem. This research was supported by NSF grant DMS-090576

On rank functions for heaps

Motivated by work of Stembridge, we study rank functions for Viennot's heaps of pieces. We produce a simple and sufficient criterion for a heap to be a ranked poset and apply the results to the heaps arising from fully commutative words in Coxeter groups.Comment: 18 pages AMSTeX, 3 figure