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2018

Kerov functions revisited

Mironov, A., Morozov, A.

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The Schur functions play a crucial role in the modern description of HOMFLY polynomials for knots and of topological vertices in DIM-based network theories, which could merge into a unified theory still to be developed.

The Macdonald functions do the same for hyperpolynomials and refined vertices, but merging appears to be more problematic.
For a detailed study of this problem, more knowledge is needed about the Macdonald polynomials than is usually available.
As a preparation for the discussion of the knot/vertices relation, we summarize the relevant facts and open problems about the Macdonald and, more generally, Kerov functions.

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