4 papers
math.GT2026
Multivariate writhe polynomial of multi-virtual knots
Zhiyun Cheng
In this paper, we extend the writhe polynomial invariant from virtual knots to multi-virtual knots. Several questions asked in [16] have been answered.
math.CO2025
Partial-dual genus polynomial of graphs
Zhiyun Cheng
Recently, Chmutov introduced the partial duality of ribbon graphs, which can be regarded as a generalization of the classical Euler-Poincaré duality. The partial-dual genus polynom…
math.GT2024
The necessity of (co)unit in nearly Frobenius algebra
Zhiyun Cheng, Ziyi Lei
In this article, we concern the concept of nearly Frobenius algebra, which corresponds to most 2D-TQFT of which each cobordism admits no critical points of index 0 or 2. We prove t…
math.GT2024
A categorification for the partial-dual genus polynomial
Zhiyun Cheng, Ziyi Lei
The partial-dual genus polynomial of a ribbon graph is the generating function that enumerates all partial duals of . In this paper, we give a ca…