On super-strong Wilf equivalence classes of permutations

Hadjiloucas, Demetris, Michos, Ioannis and Savvidou, Christina (2018) On super-strong Wilf equivalence classes of permutations. Electronic Journal of Combinatorics (E-JC), 25 (2). ISSN 1077-8926

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Official URL: https://doi.org/10.37236/6808


Super-strong Wilf equivalence is a type of Wilf equivalence on words that was originally introduced as strong Wilf equivalence by Kitaev et al. [Electron. J. Combin. 16(2)] in 2009. We provide a necessary and sufficient condition for two permutations in n letters to be super-strongly Wilf equivalent, using distances between letters within a permutation. Furthermore, we give a characterization of such equivalence classes via two-colored binary trees. This allows us to prove, in the case of super-strong Wilf equivalence, the conjecture stated in the same article by Kitaev et al. that the cardinality of each Wilf equivalence class is a power of 2.

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