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

Abstract

If V is the vertex sequence of a symmetric 2t-cycle in the hypercube graph with the vertices {1,-1}^t, then for any vertex T of the graph there exists a unique inclusion-minimal subset of V such that T is the sum of its elements. We present a simple combinatorial statistic on decompositions of vertices of the hypercube graphs with respect to symmetric cycles and describe their basic metric properties.

10 pages; v.2,3 - minor improvements; v.4 - appendix and references added

References in corpus (6)

• Combinatorial Alexander Duality -- a Short and Elementary Proof
• On the number of combinations without certain separations
• The local $h$-polynomial of the edgewise subdivision of the simplex
• Compatible polynomials and edgewise subdivisions
• Pattern Recognition on Oriented Matroids: Topes and Critical Committees
• Pattern Recognition on Oriented Matroids: Critical Committees and Distance Signals

Cited by in corpus (2)

• The Increasing Families of Sets Generated by Self-dual Clutters
• Pattern Recognition on Oriented Matroids: Subtopes and Decompositions of (Sub)topes