Several authors have examined connections among 132-avoiding permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we find analogues for some of these results for permutations π avoiding 132 and 1223 (there is no occurrence πi < πj < πj+1 such that 1 ≤ i ≤ j − 2) and provide a combinatorial interpretation for such permutations in terms of lattice paths. Using tools developed to prove these analogues, we give enumerations and generating functions for… CONTINUE READING