On algorithmic Coxeter spectral analysis of positive posets

Marcin Ga̧siorek

Applied Mathematics and Computation, 2020, vol. 386, issue C

Abstract: Following a general framework of Coxeter spectral analysis of signed graphs Δ and finite posets I introduced by Simson (SIAM J. Discrete Math. 27:827–854, 2013) we present efficient numerical algorithms for the Coxeter spectral study of finite posets I=({1,…,n},⪯I) that are positive in the sense that the symmetric Gram matrix GI:=12(CI+CItr)∈Mn(Q) is positive definite, where CI∈Mn(Z) is the incidence matrix of I encoding the relation ⪯I. In the framework of scientific computing we present a complete Coxeter spectral classification of finite positive posets I of size n=|I|<20. It extends one of the main results obtained in Ga̧siorek et al. (Eur. J. Comb. 48:127–142, 2015) for posets of size n ≤ 10. We also show that the connectivity of such posets I is determined by the complex Coxeter spectrum speccI⊆C; equivalently, by the Coxeter polynomial coxI(t)∈Z[t] od I.

Keywords: positive poset; edge-bipartite graph; spectral graph theory; Dynkin type; Coxeter spectrum; numerical algorithm (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304653

DOI: 10.1016/j.amc.2020.125507

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