The A-like matrices for a hypercube

DOI10.13001/1081-3810.1475zbMATH Open1252.05221arXiv1010.2606OpenAlexW2963093717MaRDI QIDQ3165152

Štefko Miklavič, Paul Terwilliger

Publication date: 25 October 2012

Published in: The Electronic Journal of Linear Algebra (Search for Journal in Brave)

Abstract: Let $D$ denote a positive integer and let $Q_D$ denote the graph of the $D$-dimensional hypercube. Let $X$ denote the vertex set of $Q_D$ and let $AinMX$ denote the adjacency matrix of $Q_D$. A matrix $BinMX$ is called $A$-{em like} whenever both (i) $BA=AB$; (ii) for all $x,yinX$ that are not equal or adjacent, the $(x,y)$-entry of $B$ is zero. Let $Al$ denote the subspace of $MX$ consisting of the $A$-like elements. We decompose $Al$ into the direct sum of its symmetric part and antisymmetric part. We give a basis for each part. The dimensions of the symmetric part and antisymmetric part are $D+1$ and $Dchoose2$, respectively.

Full work available at URL: https://arxiv.org/abs/1010.2606

File on IPFS (Hint: this is only the Hash - if you get a timeout, this file is not available on our server.)

zbMATH Keywords

distance-regular graphshypercubes\(A\)-like matrices

Mathematics Subject Classification ID

Hypergraphs (05C65) Association schemes, strongly regular graphs (05E30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

This page was built for publication: The A-like matrices for a hypercube

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q3165152)