On even generalized table algebras

Z. Arad, Y. Erez, M. Muzychuk

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Generalized table algebras were introduced in Arad, Fisman and Muzychuk (Israel J. Math. 114 (1999), 29-60) as an axiomatic closure of some algebraic properties of the Bose-Mesner algebras of association schemes. In this note we show that if all non-trivial degrees of a generalized integral table algebra are even, then the number of real basic elements of the algebra is bounded from below (Theorem 2.2). As a consequence we obtain some interesting facts about association schemes the non-trivial valencies of which are even. For example, we proved that if all non-identical relations of an association scheme have the same valency which is even, then the scheme is symmetric.

Original languageEnglish
Pages (from-to)163-170
Number of pages8
JournalJournal of Algebraic Combinatorics
Issue number2
StatePublished - 1 Mar 2003
Externally publishedYes


  • Association schemes
  • Generalized table algebras

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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