Callan, David and Mansour, Toufik and Shattuck, Mark - Wilf classification of triples of 4-letter patterns II

dmtcs:3219 - Discrete Mathematics & Theoretical Computer Science, March 24, 2017, Vol 19 no. 1
Wilf classification of triples of 4-letter patterns II

Authors: Callan, David and Mansour, Toufik and Shattuck, Mark

This is the second of two papers in which we determine all 242 Wilf classes of triples of 4-letter patterns by showing that there are 32 non-singleton Wilf classes. There are 317 symmetry classes of triples of 4-letter patterns and after computer calculation of initial terms, the problem reduces to showing that counting sequences that appear to be the same (agree in the first 16 terms) are in fact identical. This amounts to counting avoiders for 107 representative triples. The insertion encoding algorithm (INSENC) applies to many of them and some others have been previously counted. There remain 36 triples and the first paper dealt with the first 18. In this paper, we find the generating function for the last 18 triples which turns out to be algebraic in each case. Our methods are both combinatorial and analytic, including decomposi-tions by left-right maxima and by initial letters. Sometimes this leads to an algebraic equation for the generating function, sometimes to a functional equation or a multi-index recurrence that succumbs to the kernel method. A particularly nice so-called cell decomposition is used in one of the cases (Case 238).


Source : oai:HAL:hal-01321517v3
Volume: Vol 19 no. 1
Section: Combinatorics
Published on: March 24, 2017
Submitted on: March 24, 2017
Keywords: pattern avoidance,insertion encoding algorithm,kernel method,Wilf-equivalence,[MATH] Mathematics [math]


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