Spin models for link polynomials, strongly regular graphs and Jaeger’s Higman-Sims model
نویسندگان
چکیده
منابع مشابه
Spin Models for Link Polynomials, Strongly Regular Graphs and Jaeger's Higman-sims Model
We recall first some known facts on Jones and Kauffman polynomials for links, and on state models for link invariants. We give next an exposition of a recent spin model due to F. Jaeger and which involves the Higman-Sims graph. The associated invariant assigns to an oriented link the evaluation for a = τ 5 and z = 1 of its Kauffman polynomial in the Dubrovnik form, where τ denotes the golden ra...
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We introduce some well known results about permutation groups, strongly regular graphs, design theory and finite geometry. Our goal is the construction of the Higman-Sims group as an index 2 subgroup of the automorphism group of a (100, 22, 0, 6)-srg. To achieve this we introduce some tools from design theory. Some of the arguments here are slightly more general than those given in lectures. Al...
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We propose a new elementary definition of the Higman-Sims graph in which the 100 vertices are parametrised with Z4 × Z5 × Z5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson’s pentagonpentagram definition of the Hoffman-Singleton graph and is obtained by studying maximum cocliques of the Hoffman-Singleton graph in Robertson’s parametrisation. Th...
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It has been known for some time that the Higman-Sims graph can be decomposed into the disjoint union of two Hoffman-Singleton graphs. In this paper we establish that the Higman-Sims graph can be edge decomposed into the disjoint union of 5 double-Petersen graphs, each on 20 vertices. It is shown that in fact this can be achieved in 36960 distinct ways. It is also shown that these different ways...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1994
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1994.162.57