2023/12/28 by Gurvan Mével, Mével, Gurvan
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Multimedia Learning Systems #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2312.16871
openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2022, Brugallé and Jaramillo-Puentes showed that the coefficients of small codegree of the tropical refined invariant are polynomial in the Newton polygon. This raised the question of the existence of universal polynomials giving these coefficients, i.e. polynomials depending only on the genus and the codegree, and with variables the combinatorial data of the Newton polygon.In this paper we show that such universal polynomials exist for rational enumeration, and we give an explicit formula. The proof relies on the manipulation of floor diagrams.