A Bijection for Tricellular Maps

Hillary S. W. Han, Christian M. Reidys
2013 ISRN Discrete Mathematics  
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
more » ... genus g into unicellular, bicellular or tricellular maps of strictly lower genera. The bijection employs edge cutting, edge contraction, and edge deletion.
doi:10.1155/2013/712431 fatcat:lzrcjoyp3jc2flznicec4xr5pu