منابع مشابه
Coherent configurations
In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as t...
متن کاملThe Absolute Bound for Coherent Configurations
In this paper we generalize the absolute bound for association schemes to coherent configurations. We examine this bound in the context of quasi-symmetric and strongly regular designs. In particular, we use it to derive a new feasibility condition for strongly regular designs and give examples of parameter sets ruled out by this condition but which pass all other feasibility conditions known to...
متن کاملFast matrix multiplication using coherent configurations
We introduce a relaxation of the notion of tensor rank, called s-rank, and show that upper bounds on the s-rank of the matrix multiplication tensor imply upper bounds on the ordinary rank. In particular, if the “s-rank exponent of matrix multiplication” equals 2, then ω = 2. This connection between the s-rank exponent and the ordinary exponent enables us to significantly generalize the group-th...
متن کاملTightness in subset bounds for coherent configurations
Association schemes have many applications to the study of designs, codes and geometries, and are well-studied. Coherent configurations are a natural generalization of association schemes, however, analogous applications have yet to be fully explored. Recently, Hobart [Michigan Math. J. 58 (2009), 231–239] generalized the linear programming bound for association schemes, showing that a subset Y...
متن کاملStructure and automorphisms of primitive coherent configurations
Coherent configurations (CCs) are highly regular colorings of the set of ordered pairs of a “vertex set”; each color represents a “constituent digraph.” CCs arise in the study of permutation groups, combinatorial structures such as partially balanced designs, and the graph isomorphism problem; their history goes back to Schur in the 1930s. A CC is primitive (PCC) if all its constituent digraphs...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 1975
ISSN: 0046-5755,1572-9168
DOI: 10.1007/bf00147398