2021/08/03 by Qi Yan, Yan, Qi, Xian’an Jin +1 · 1 citation
Mathematics · #05B35 #05C10 #05C31 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2108.01263
openalex publication_date 2021/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Gross, Mansour and Tucker introduced the partial duality polynomial of a ribbon graph and posed a conjecture that there is no orientable ribbon graph whose partial duality polynomial has only one non-constant term. We found an infinite family of counterexamples for the conjecture and showed that essentially these are the only counterexamples. This is also obtained independently by Chumutov and Vignes-Tourneret and they posed a problem: it would be interesting to know whether the partial duality polynomial and the related conjectures would make sence for general delta-matroids. In this paper, we show that partial duality polynomials have delta-matroid analogues. We introduce the twist polynomials of delta-matroids and discuss its basic properties for delta-matroids. We give a characterization of even normal binary delta-matroids whose twist polynomials have only one term and then prove that the twist polynomial of a normal binary delta-matroid contains non-zero constant term if and only if its intersection graph is bipartite.