A generalization of the Kreweras triangle through the universal $\text{sl}_2$ weight system

TL;DR

This paper introduces a new family of polynomials that generalize the Kreweras triangle and explores their connection to the universal sl2 weight system in knot theory, revealing new combinatorial structures.

Contribution

It defines a novel family of polynomials extending the Kreweras triangle and demonstrates their role within the universal sl2 weight system for knot invariants.

Findings

Generalization of the Kreweras triangle through new polynomials

Connection established between these polynomials and the sl2 weight system

Insight into combinatorial structures underlying knot invariants

Abstract

In the theory of finite order knot invariants, the universal $\text{sl}_2$ weight system maps the chord diagrams to polynomials in a single variable with integer coefficients. In this paper, we define a family of polynomials that generalize the Kreweras triangle (known to refine the normalized median Genocchi numbers), and we show how it appears in this weight system.