A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves a formula for Kontsevich-Witten tau-function using Schur Q-polynomials.
Classifies trees with strictly unimodal q-polynomials.
Paper proves BGW tau-function can be represented as Q-polynomials.
Qazaqzeh and Chbili showed that for any quasi-alternating link, the degree of -polynomial is less than its determinant. We give a refinement of their evaluation.
New formulas for knot polynomial evaluations from covering spaces.
This is an extended abstract of the talk given at the Oberwolfach Workshop "Algebraic Structures in Low-Dimensional Topology", 25 May -- 31 May 2014. My goal was to describe progress in distributive homology from the previous Oberwolfach Workshop June 3 - June 9, 2012, in particular my work on Yang-Baxter homology; how…
Let be a signed graph. Let be the graph obtained from by replacing each edge by a chain or a sheaf. We first establish a relation between the -polynomial of [6] and the -polynomial of [9]. Two special dual cases are derived from the relation, one of which has been studied in [8]…
Given any unoriented link diagram, a group of new knot invariants are constructed. Each of them satisfies a generalized 4 term skein relation. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations of such a ring defines new link invariants. In this sense, they produce the well…
We describe in this note a new invariant of rooted trees. We argue that the invariant is interesting on it own, and that it has connections to knot theory and homological algebra. However, the real reason that we propose this invariant to readers is that we deal here with an elementary, interesting, new mathematics, an…
The paper studies polynomials and ideals from colored Jones polynomials for links.
Quantum theory constructs a group and skein module for knot complements.
Researchers found a -series identity for a specific knot using representations.
Three-layer neural networks learn hierarchical polynomial functions efficiently.