Geodesic
Refining enumeration schemes to count according to permutation statistics
Andrew M. Baxter1
1Pennsylvania State University, University Park
The electronic journal of combinatorics, Tome 21 (2014) no. 2
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We develop algorithmic tools to compute quickly the distribution of permutation statistics over sets of pattern-avoiding permutations. More specfically, the algorithms are based on enumeration schemes, the permutation statistics are based on the number of occurrences of certain vincular patterns, and the permutations avoid sets of vincular patterns. We prove that whenever a finite enumeration scheme exists to count the number of pattern-avoiding permutations, then the distribution of statistics like the number of descents can also be computed based on the same scheme. Statistics such as the number of peaks, right-to-left maxima, and the major index are also investigated, as well as multi-statistics.
DOI : 10.37236/4002
Classification : 05A15, 05A19, 05A05
Mots-clés : pattern avoidance, automated discovery, permutation statistics, consecutive pattern, vincular pattern

Andrew M. Baxter  1

1 Pennsylvania State University, University Park 
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     title = {Refining enumeration schemes to count according to permutation statistics},
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     year = {2014},
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Andrew M. Baxter. Refining enumeration schemes to count according to permutation statistics. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/4002

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