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

From This Paper

Topics from this paper.
5 Citations
12 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 12 references

Circulant Matrices

  • P. J. Davis
  • 2nd ed., Chelsea
  • 1994
1 Excerpt

Isomorphism problem for a class of point-symmetric structures

  • L. Babai
  • Acta Math. Ada. Sci. Hung. 29
  • 1977
1 Excerpt

Djoković , Isomorphism problem for a special class of graphs , Acta Math

  • J. Turner
  • Acad . Sci . Hung .
  • 1970

Graphs with circulant adjacency matrices

  • B. Elspas, J. Turner
  • J. Comb. Th. 9
  • 1970
2 Excerpts

Similar Papers

Loading similar papers…