In 2012, Sagan and Savage introduced the notion of st-Wilf equivalence for
a statistic st and for sets of permutations that avoid particular permutation
patterns which can be extended to generalized permutation patterns. In this
paper we consider inv-Wilf equivalence on sets of two or more consecutive
permutation patterns. We say that two sets of generalized permutation patterns
Πand Π′ are inv-Wilf equivalent if the generating function for the
inversion statistic on the permutations that simultaneously avoid all elements
of Î is equal to the generating function for the inversion statistic on the
permutations that simultaneously avoid all elements of Π′.
In 2013, Cameron and Killpatrick gave the inversion generating function for
Fibonacci tableaux which are in one-to-one correspondence with the set of
permutations that simultaneously avoid the consecutive patterns 321 and
312. In this paper, we use the language of Fibonacci tableaux to study the
inversion generating functions for permutations that avoid Î where Î is
a set of five or fewer consecutive permutation patterns. In addition, we
introduce the more general notion of a strip tableaux which are a useful
combinatorial object for studying consecutive pattern avoidance. We go on to
give the inversion generating functions for all but one of the cases where
Î is a subset of three consecutive permutation patterns and we give several
results for Î a subset of two consecutive permutation patterns