Geodesic
The initial involution patterns of permutations
The electronic journal of combinatorics, Tome 14 (2007)
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For a permutation $\pi=\pi_1\pi_2\cdots\pi_n\in S_n$ and a positive integer $i\leq n$, we can view $\pi_1\pi_2\cdots\pi_i$ as an element of $S_i$ by order-preserving relabeling. The $j$-set of $\pi$ is the set of $i$'s such that $\pi_1\pi_2\cdots\pi_i$ is an involution in $S_i$. We prove a characterization theorem for $j$-sets, give a generating function for the number of different $j$-sets of permutations in $S_n$. We also compute the numbers of permutations in $S_n$ with a given $j$-set and prove some properties of them.
DOI : 10.37236/921
Classification : 05A05, 05A15
Mots-clés : generating function 
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     author = {Dongsu Kim and Jang Soo Kim},
     title = {The initial involution patterns of permutations},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/921},
     zbl = {1111.05003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/921/}
}
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Dongsu Kim; Jang Soo Kim. The initial involution patterns of permutations. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/921

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