On two determinants with interesting factorizations

Alina Copeland,Frank Schmidt,Rodica Simion

Discrete Mathematics（2002）

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摘要

We show that two determinants arising in different mathematical contexts, both exhibiting striking factorization properties, are in fact related. These are the determinants of the matrix of chromatic joins and of the matrix associated with Lickorish's bilinear form in the study of invariants for 3-manifolds. We show that the two determinants are essentially equal up to a change of variable and that they are related to a determinant arising in the representation theory for type A Hecke algebras.

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关键词

chromatic joins,gram matrix,different mathematical context,determinant,hecke algebra,meander,noncrossing partition,bilinear form,striking factorization property,representation theory,interesting factorization

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