Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. V

Abstract

We consider decompositions of topes of the oriented matroid realizable as the arrangement of coordinate hyperplanes in ${\mathbb{R}}^{2^t}$, with respect to a distinguished symmetric $2\cdot 2^t$-cycle in its hypercube graph of topes $\mathbf{H}(2^t,2)$. We seek interpretations of such decompositions in the context of subset families on the ground set $E_t:=\{1,\dots ,t\}$ and of the families of their blocking sets, in the context of clutters on $E_t$ and of their blockers.

46 pages; v.2,3 - notation explained, misprints corrected, and references added; v.4-6 - more misprints corrected, main notation changed for better readability, minor improvements