2018/01/15 by Rinat Kashaev, Kashaev, Rinat
Mathematics · Chemistry · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Molecular spectroscopy and chirality
paper · pdf · doi:10.48550/arxiv.1801.04632
Let D be an oriented link diagram with the set of regions rD. We define a symmetric map (or matrix) \operatornameτD\colonrD× rD → ℤ[x] that gives rise to an invariant of oriented links, based on a slightly modified S-equivalence of Trotter and Murasugi in the space of symmetric matrices. In particular, for real x, the negative signature of \operatornameτD corrected by the writhe is conjecturally twice the Tristram--Levine signature function, where 2x=√(t)+\frac1√(t) with t being the indeterminate of the Alexander polynomial.