A Bijection for Tricellular Maps. (8th December 2013)

• Record Type: Journal Article
• Authors: Han, Hillary S. W.; Reidys, Christian M.
• Other Names: Kelarev A. Academic Editor.; Smyth W. F. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2013(2013)
• Publication Date: 2013-12-08
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2013/712431
• Languages: English
• ISSNs: 2090-7788

Abstract

Abstract : We give a bijective proof for a relation between unicellular, bicellular, and tricellular maps. These maps represent cell complexes of orientable surfaces having one, two, or three boundary components. The relation can formally be obtained using matrix theory (Dyson, 1949) employing the Schwinger-Dyson equation (Schwinger, 1951). In this paper we present a bijective proof of the corresponding coefficient equation. Our result is a bijection that transforms a unicellular map of genus g into unicellular, bicellular or tricellular maps of strictly lower genera. The bijection employs edge cutting, edge contraction, and edge deletion.