Equivalence of Sparse Circulants: the Bipartite Ádám Problem

@inproceedings{Zieve2007EquivalenceOS,
title={Equivalence of Sparse Circulants: the Bipartite Ádám Problem},
author={Michael E. Zieve},
year={2007}
}

We consider n-by-n circulant matrices having entries 0 and 1. Such matrices can be identified with sets of residues mod n, corresponding to the columns in which the top row contains an entry 1. Let A and B be two such matrices, and suppose that the corresponding residue sets SA, SB have size at most 3. We prove that the following are equivalent: (1) there are integers u, v mod n, with u a unit, such that SA = uSB + v; (2) there are permutation matrices P, Q such that A = PBQ. Our proof relies… CONTINUE READING