Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns
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.
