2024/04/18 by Blas Fernández, Fernández, Blas, Roghayeh Maleki +5
Computer Science · Engineering · Mathematics · #05C50 #05E99 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2404.12510
openalex publication_date 2024/04/18 · openalex created_date 2024/04/23 · openalex updated_date 2026/07/28
The Q-polynomial property is an algebraic property of distance-regular graphs, that was introduced by Delsarte in his study of coding theory. Many distance-regular graphs admit the Q-polynomial property. Only recently the Q-polynomial property has been generalized to graphs that are not necessarily distance-regular. In [ J. Combin. Theory Ser. A, 205:105872, 2024 ], it was shown that graphs arising from the Hasse diagrams of the so-called attenuated space posets are Q-polynomial. These posets could be viewed as q-analogs of the Hamming posets, which were not studied in [ J. Combin. Theory Ser. A, 205:105872, 2024 ]. The main goal of this paper is to fill this gap by showing that the graphs arising from the Hasse diagrams of the Hamming posets are Q-polynomial.