English

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

Combinatorics 2018-11-08 v4

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.

Keywords

Cite

@article{arxiv.1511.07024,
  title  = {Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs},
  author = {Andrey O. Matveev},
  journal= {arXiv preprint arXiv:1511.07024},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-22T11:51:32.427Z