## Abstract

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 language | English |
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Pages (from-to) | 163-170 |

Number of pages | 8 |

Journal | Journal of Algebraic Combinatorics |

Volume | 17 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2003 |

### Bibliographical note

Funding Information:†The contribution of this author to this paper is a part of his Ph.D. thesis at Bar-Ilan University. ∗This author was partially supported by the Israeli Ministry of Absorption.

## Keywords

- Association schemes
- Generalized table algebras