A Tutte polynomial for maps II: The non-orientable case. (May 2020)

• Record Type: Journal Article
• Authors: Goodall, Andrew; Litjens, Bart; Regts, Guus; Vena, Lluís
• Is Part Of: European journal of combinatorics. Volume 86(2020)
• Publication Date: 2020-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2020.103095
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We construct a new polynomial invariant of maps (graphs embedded in a closed surface, orientable or non-orientable), which contains as specializations the Krushkal polynomial, the Bollobás—Riordan polynomial, the Las Vergnas polynomial, and their extensions to non-orientable surfaces, and hence in particular the Tutte polynomial. Other evaluations include the number of local flows and local tensions taking non-identity values in a given finite group.