Han's Bijection via Permutation Codes

Details Han's Bijection via Permutation Codes Han's Bijection via Permutation Codes

2010-04-19

arxiv.org/abs/1004.3202v2

Mathematics

Combinatorics

12 pages, to appear in European J. Combin

Scientific paper

We show that Han's bijection when restricted to permutations can be carried out in terms of the cyclic major code and the cyclic inversion code. In other words, it maps a permutation $\pi$ with a cyclic major code $(s_1, s_2, ..., s_n)$ to a permutation $\sigma$ with a cyclic inversion code $(s_1,s_2, ..., s_n)$. We also show that the fixed points of Han's map can be characterized by the strong fixed points of Foata's second fundamental transformation. The notion of strong fixed points is related to partial Foata maps introduced by Bj\"orner and Wachs.

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