vix.ing · top · new · best · stats · spec

A q-analog of the adjacency matrix of the n-cube

2022/04/12 by Subhajit Ghosh, Ghosh, Subhajit, Murali K. Srinivasan +1
Mathematics · #05C81 #05E18 #20C30 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2204.05540

openalex publication_date 2022/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a q-analog of the adjacency matrix of the n-cube, determine its eigenvalues and write down a canonical eigenbasis. We give a weighted count of the number of rooted spanning trees in the q-analog of the n-cube. Remarks on the previous version: The q-analog of the Kac matrix appears in Terwilliger's classification of Leonard pairs and as such its eigenvalues and eigenvectors were known. Reference added to Terwilliger's papers and also to a paper of Johnson. Title changed to reflect this.

Related