Inversion sequences and signed permutations

A signed inversion sequence of length n is a sequence of integers e = e(1) <middle dot> <middle dot> <middle dot> e(n) , where e(i +1) is an element of {0, 0<overline>,1,1<overline>,. . . , i, i<overline>} for every i is an element of {0, 1, ... , n - 1} . For a set of signed patterns B , let I-n<overline>(B) <overline> n (B) be the set of signed inversion sequences of length n that avoid all the signed patterns from B . We say that two sets of signed patterns B and C are Wilf-equivalent if |I-n<overline>(B)| = In<overline> (c) for every n > 0 . In this paper, by generating trees, we show that the number of Wilf-equivalences among singles of a length-2 2 signed pattern is 3 and the number of Wilf-equivalences among pairs of a length-2 signed patterns is 30 .