Abstract | ||
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The partial dual GA with respect to a subset A of edges of a ribbon graph G was introduced by Chmutov in connection with the Jones–Kauffman and Bollobás–Riordan polynomials, and it has developed into a topic of independent interest. This paper studies, for a given G, the enumeration of the partial duals of G by Euler genus, as represented by its generating function, which we call the partial-dual Euler-genus polynomial of G. A recursion is given for subdivision of an edge and is used to derive closed formulas for the partial-dual genus polynomials of four families of ribbon graphs. The log-concavity of these polynomials is studied in some detail. We include a concise, self-contained proof that χ(GA)=χ(A)+χ(E(G)−A)−2|V(G)|, where χ(G)=|V(G)|−|E(G)|+|F(G)|, and where A represents the ribbon graph obtained from G by deleting all edges not in A. This formula is a variant of a result of Moffatt. |
Year | DOI | Venue |
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2020 | 10.1016/j.ejc.2020.103084 | European Journal of Combinatorics |
DocType | Volume | ISSN |
Journal | 86 | 0195-6698 |
Citations | PageRank | References |
0 | 0.34 | 11 |
Authors | ||
3 |
Name | Order | Citations | PageRank |
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Jonathan L. Gross | 1 | 458 | 268.73 |
Toufik Mansour | 2 | 423 | 87.76 |
Thomas W. Tucker | 3 | 191 | 130.07 |