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

2015/11/22 by Andrey O. Matveev, Matveev, Andrey O.
Computer Science · #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #Data Management and Algorithms #FOS: Mathematics #Graph Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1511.07024

openalex publication_date 2015/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Identifying the Minimal Transversals of a Hypergraph and Related Problems
• New Results on Monotone Dualization and Generating Hypergraph Transversals
• A theory of diagnosis from first principles
• Compatible polynomials and edgewise subdivisions

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