A wreath product is a method to construct an association scheme from two association schemes. We determine the automorphism group of a wreath product. We show a known result that a wreath product is Schurian if and only if both components are Schurian, which yields large families of non-Schurian association schemes and non-Schurian $S$-rings. We also study iterated wreath products. Kernel schemes by Martin and Stinson are shown to be iterated wreath products of class-one association schemes. The iterated wreath products give examples of projective systems of non-Schurian association schemes, with an explicit description of primitive idempotents.
@article{10_37236_11414,
author = {Makoto Matsumoto and Kento Ogawa},
title = {Wreath products and projective system of {non-Schurian} association schemes},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {1},
doi = {10.37236/11414},
zbl = {1554.05184},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11414/}
}
TY - JOUR
AU - Makoto Matsumoto
AU - Kento Ogawa
TI - Wreath products and projective system of non-Schurian association schemes
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/11414/
DO - 10.37236/11414
ID - 10_37236_11414
ER -
%0 Journal Article
%A Makoto Matsumoto
%A Kento Ogawa
%T Wreath products and projective system of non-Schurian association schemes
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/11414/
%R 10.37236/11414
%F 10_37236_11414
Makoto Matsumoto; Kento Ogawa. Wreath products and projective system of non-Schurian association schemes. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/11414
