4 papers
A dimer view on Fox's trapezoidal conjecture
Karola Mészáros, Melissa Sherman-Bennett, Alexander Vidinas
Fox's conjecture (1962) states that the sequence of absolute values of the coefficients of the Alexander polynomial of alternating links is trapezoidal. While the conjecture remain…
On the Alexander polynomial of special alternating links
Elena S. Hafner, Karola Mészáros, Alexander Vidinas
The Alexander polynomial (1928) is the first polynomial invariant of links devised to help distinguish links up to isotopy. Fox's conjecture (1962) -- stating that the absolute val…
Trapezodial property of the generalized Alexander polynomial
Tamás Kálmán, Karola Mészáros, Alexander Postnikov
Fox's conjecture from 1962, that the absolute values of the coefficients of the Alexander polynomial of an alternating link are trapezoidal, has remained stubbornly open to this da…
Dimer face polynomials in knot theory and cluster algebras
Karola Mészáros, Gregg Musiker, Melissa Sherman-Bennett +1
The set of perfect matchings of a connected bipartite plane graph has the structure of a distributive lattice, as shown by Propp, where the partial order is induced by the heig…