Abstract
In this paper, we study the computation complexity of some algebraic combinatorial problems that are closely associated with the graph isomorphism problem. The key point of our considerations is a relation algebra which is a combinatorial analog of a cellular algebra. We present upper bounds on the complexity of central algorithms for relation algebras such as finding the standard basis of extensions and intersection of relation algebras. Also, an approach is described to the graph isomorphism problem involving Schurian relation algebras (these algebras arise from the centralizing rings of permutation groups). We also discuss a number of open problems and possible directions for further investigation. Bibliography: 18 titles.
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Translated by I. N.Ponomarenko.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol 202, 1992, pp. 116–134.
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Ponomarenko, I.N. On computation complexity problems concerning relation algebras. J Math Sci 79, 1105–1114 (1996). https://doi.org/10.1007/BF02366131
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DOI: https://doi.org/10.1007/BF02366131