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,-1t, 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.
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