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Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2022

Self-Dual Maps I: Antipodality

Résumé

A self-dual map is said to be antipodally self-dual if the dual map is antipodal embedded in with respect to . In this paper, we investigate necessary and/or sufficient conditions for a map to be antipodally self-dual. In particular, we present a combinatorial characterization for map to be antipodally self-dual in terms of certain involutive labelings. The latter lead us to obtain necessary conditions for a map to be strongly involutive (a notion relevant for its connection with convex geometric problems). We also investigate the relation of antipodally self-dual maps and the notion of antipodally symmetric maps. It turns out that the latter is a very helpful tool to study questions concerning the symmetry as well as the amphicheirality of links.
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Dates et versions

hal-04524667 , version 1 (28-03-2024)

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Luis Montejano, Jorge Luis Ramírez Alfonsín, Ivan Rasskin. Self-Dual Maps I: Antipodality. SIAM Journal on Discrete Mathematics, 2022, 36 (3), pp.1551-1566. ⟨10.1137/20M1367076⟩. ⟨hal-04524667⟩
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