Enumeration of small Wilf classes avoiding 1342 and two other 4-letter
patterns
release_vvghd5zmj5dytjhi6jmiclrs6a
by
David Callan, Toufik Mansour
2017
Abstract
This paper is one of a series whose goal is to enumerate the avoiders, in the
sense of classical pattern avoidance, for each triple of 4-letter patterns.
There are 317 symmetry classes of triples of 4-letter patterns, avoiders of 267
of which have already been enumerated. Here we enumerate avoiders for all small
Wilf classes that have a representative triple containing the pattern 1342,
giving 40 new enumerations and leaving only 13 classes still to be enumerated.
In all but one case, we obtain an explicit algebraic generating function that
is rational or of degree 2. The remaining one is shown to be algebraic of
degree 3. We use standard methods, usually involving detailed consideration of
the left to right maxima, and sometimes the initial letters, to obtain an
algebraic or functional equation for the generating function.
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