Nonexistence of Certain Skew-symmetric Amorphous Association Schemes
Abstract
An association scheme is amorphous if it has as many fusion schemes as possible. Symmetric amorphous schemes were classified by A. V. Ivanov [A. V. Ivanov, Amorphous cellular rings II, in Investigations in algebraic theory of combinatorial objects, pages 39--49. VNIISI, Moscow, Institute for System Studies, 1985] and commutative amorphous schemes were classified by T. Ito, A. Munemasa and M. Yamada [T. Ito, A. Munemasa and M. Yamada, Amorphous association schemes over the Galois rings of characteristic 4, European J. Combin., 12(1991), 513--526]. A scheme is called skew-symmetric if the diagonal relation is the only symmetric relation. We prove the nonexistence of skew-symmetric amorphous schemes with at least 4 classes. We also prove that non-symmetric amorphous schemes are commutative.
Keywords
Cite
@article{arxiv.0909.3755,
title = {Nonexistence of Certain Skew-symmetric Amorphous Association Schemes},
author = {Jianmin Ma},
journal= {arXiv preprint arXiv:0909.3755},
year = {2010}
}
Comments
10 pages