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This is an expository paper extending the tutorial talk at the MATRIX Workshop on Uniqueness and Discernment in Graph Polynomials in October 2023. The explanation is mainly based on the paper ``Partial Duality of Hypermaps" by S.Chmutov and F.Vignes-Tourneret with maximal possible simplifications.
Sergei Chmutov (Sat,) studied this question.
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