1. On p-schemes with the same degrees of thin radical and thin residue
- Author
-
Fatemeh Raei Barandagh and Amir Rahnamai Barghi
- Subjects
Combinatorics ,Residue (complex analysis) ,Association scheme ,genetic structures ,Wreath product ,General Mathematics ,Prime number ,Valency ,sense organs ,Association scheme,p-scheme,thin radical,thin residue ,eye diseases ,Mathematics - Abstract
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.
- Published
- 2015