منابع مشابه
Crested Products of Association Schemes
In this paper, we define a new type of product of association schemes (and of the related objects, permutation groups and orthogonal block structures), which generalizes the direct and wreath products (which are referred to as “crossing” and “nesting” in the statistical literature.) Given two association schemes Qr for r = 1, 2, each having an inherent partition Fr (that is, a partition whose e...
متن کاملSemidirect Products of Association Schemes
In his 1996 work developing the theory of association schemes as a ‘generalized’ group theory, Zieschang introduced the concept of the semidirect product as a possible product operation of certain association schemes. In this paper we extend the semidirect product operation into the entire set of association schemes. We then derive a way to decompose certain association schemes into smaller ass...
متن کاملCrested Products of Markov Chains
In this work we define two kinds of crested product for reversible Markov chains, which naturally appear as a generalization of the case of crossed and nested product, as in association schemes theory, even if we do a construction that seems to be more general and simple. Although the crossed and nested product are inspired by the study of Gelfand pairs associated with the direct and the wreath...
متن کاملFusion Schemes of Semidirect Products of Association Schemes
Let X = (X, H) and Y = (Y, K) be two association schemes. In [1], an (external) semidirect product Z = (X × Y, H nπ K) of Y and X relative to π is defined. In this paper, given a normal closed subset N of K which is fixed by π, we find a way to construct a fusion scheme of Z with respect to N . We then show that every association scheme obtained by any of three products, direct, wreath and semi...
متن کاملGeneralized wreath products of association schemes
Given a finite partially ordered set X, and, for each x in X, an association scheme on a set Ωx, we show how to define an association scheme on ∏ x Ωx in a way that specializes to iterated crossing and nesting when X is seriesparallel. The character table of the new association scheme is found.
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2005
ISSN: 0024-6107,1469-7750
DOI: 10.1112/s0024610705006666