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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!.
0
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
0,9
COMMENTS
For T(4,1) and T(4,2) see the references in the Callan et el. articles.
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.
EXAMPLE
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.
CROSSREFS
Cf. A099952.
Sequence in context: A128210 A215409 A239232 * A153012 A275300 A283833
KEYWORD
nonn,tabf,more
AUTHOR
N. J. A. Sloane, Jul 28 2021, based on information supplied by Toufik Mansour.
STATUS
approved