Štefko Miklavič (FAMNIT UP, Slovenija): A-like matrices of hypercubes

Datum objave: 22. 2. 2010
Seminar za teorijo grup in kombinatoriko
Četrtek, 25. 2. 2010, od 17h do 19h, učilnica 016, Pedagoška fakulteta Univerze v Ljubljani
Povzetek: Let D denote a positive integer and let Q_D denote the graph of the D-dimensional hypercube. Let A denote the adjacency matrix of Q_D. A matrix B (with the same dimensions as A) is called A-{\em like} matrix of Q_D if the following (i), (ii) hold: (i) BA = AB, and (ii) the support of B is contained in the support of A+I, where I is the identity matrix. In this talk we show that the dimension of the vector space of all A-like matrices of Q_D is D(D+1)/2 + 1.