A346624 Irregular triangle read by rows: T(n,k) is the number of distinct Wilf classes of subsets of exactly k patterns in S_n, for 0 <= k <= n!.
1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 2, 1, 1, 3, 38, 242, 1100, 3441, 8438, 15392, 19002, 16293, 10624, 5857, 3044, 1546, 786, 393, 198, 105, 55, 28, 14, 8, 4, 2, 1
Offset: 0
Examples
The rows corresponding to S_0, S_1, S_2, S_3, and S_4 are: 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 2, 1, 1, 3, 38, 242, 1100, 3441, 8438, 15392, 19002, 16293, 10624, 5857, 3044, 1546, 786, 393, 198, 105, 55, 28, 14, 8, 4, 2, 1.
References
- T. Mansour and M. Schork, Wilf classification of subsets of four letter patterns, Journal of Combinatorics and Number Theory 8:1 (2016) 1--111.
- T. Mansour and M. Schork, Wilf classification of subsets of eight and nine four-letter patterns, Journal of Combinatorics and Number Theory 8:3 (2016) 27pp.
- T. Mansour and M. Schork, Wilf classification of subsets of six and seven four-letter patterns, Journal of Combinatorics and Number Theory 9:3 (2017).
Links
- D. Callan, T. Mansour and M. Shattuck, Wilf classification of triples of 4-letter patterns I, Discrete Mathematics & Theoretical Computer Science 19:1 (2017) #5.
- D. Callan, T. Mansour and M. Shattuck, Wilf classification of triples of 4-letter patterns II, Discrete Mathematics & Theoretical Computer Science 19:1 (2017) #6.
- D. Callan, T. Mansour and M. Shattuck, Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done, Pure Mathematics and Applications 28:1 (2019) 14--69.
- T. Mansour, Enumeration and Wilf-classification of permutations avoiding five patterns of length 4, Contributions to Mathematics 1 (2020) 1--10.
- T. Mansour, Enumeration and Wilf-classification of permutations avoiding four patterns of length 4, Discrete Mathematics Letters 3 (2020) 67--94.
- Toufik Mansour, Restricted Permutations, Conjecture of Lin and Kim, and Work of Andrews and Chern, Talk presented at Workshop "Combinatorics and Algebras from Amitai Regev to Doron Zeilberger", July 26-29, 2021.
- Rodica Simion and Frank W. Schmidt, Restricted Permutations, Europ. J. Combinatorics, 6 (1985), 383-406.
Crossrefs
Cf. A099952.
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