Journal of Algebraic Combinatorics

, Volume 10, Issue 1, pp 29–45

On a New High Dimensional Weisfeiler-Lehman Algorithm

  • Sergei Evdokimov
  • Marek Karpinski
  • Ilia Ponomarenko
Article

DOI: 10.1023/A:1018672019177

Cite this article as:
Evdokimov, S., Karpinski, M. & Ponomarenko, I. Journal of Algebraic Combinatorics (1999) 10: 29. doi:10.1023/A:1018672019177

Abstract

We investigate the following problem: how different can a cellular algebra be from its Schurian closure, i.e., the centralizer algebra of its automorphism group? For this purpose we introduce the notion of a Schurian polynomial approximation scheme measuring this difference. Some natural examples of such schemes arise from high dimensional generalizations of the Weisfeiler-Lehman algorithm which constructs the cellular closure of a set of matrices. We prove that all of these schemes are dominated by a new Schurian polynomial approximation scheme defined by the m-closure operators. A sufficient condition for the m-closure of a cellular algebra to coincide with its Schurian closure is given.

graph isomorphism problem cellular algebra permutation group 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Sergei Evdokimov
    • 1
  • Marek Karpinski
    • 2
  • Ilia Ponomarenko
    • 1
  1. 1.Academy of SciencesSt. Petersburg Institute for Informatics and AutomationRussia
  2. 2.Department of Computer ScienceUniversity of BonnGermany

Personalised recommendations