Fatemeh BARAND RAEIAGH, Amir BARGHI RAHNAMAI

On p-schemes with the same degrees of thin radical and thin residue

Let p and n>1 be a prime number and an integer, respectively. In this paper, first we show that any p-scheme whose thin radical and thin residue are equal is isomorphic to a fission of the wreath product of 2 thin schemes. In addition, we characterize association p-schemes whose thin radical and thin residue each have degree equal to p. We also characterize association p-schemes on pn points whose thin radical and thin residue each have degree equal to pn-1, and whose basis relations each have valency 1 or pn-1. Moreover, we show that such schemes are Schurian.

Anahtar Kelimeler:

Association scheme, p-scheme, thin radical, thin residue

On p-schemes with the same degrees of thin radical and thin residue

Keywords:

Association scheme, p-scheme, thin radical, thin residue,

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