2013/03/21 by Andrey O. Matveev, Matveev, Andrey O.
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Neural Networks and Applications #math.CO
paper · pdf · doi:10.48550/arxiv.1303.5350
6 pages
arxiv created 2013/03/21 · openalex publication_date 2013/03/21 · arxiv updated 2013/03/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
If V(R) is the vertex sequence of a symmetric cycle R in the tope graph of a simple acyclic oriented matroid M on a t-element ground set, then the set min V(R) of minimal elements in the subposet V(R) of the tope poset of M, based at the positive tope, is a critical committee for M that votes for the base tope. We consider the sequence zR of poset ranks of the elements from the vertex sequence of R as a fragment of a signal with period 2t and relate the number of members of the committee min V(R) to the magnitudes of [t/2] components, with odd indices, of the discrete Fourier transform of the distance vector zR.