A CLASS OF P-POLYNOMIAL TABLE ALGEBRAS WITH AND WITHOUT INTEGER MULTIPLICITIES

摘要

The homogeneous, monotonic, P-polynomial table algebras with valency k ≥ 2 are classified. It is also determined which of these algebras, when integral, have integer multiplicities. In particular, it is shown that all multiplicities are integers only if k = 2 or the diameter d = 2. Some of these algebras come from distance-regular graphs, and some do not.