Generating Trees of (Reducible) 1324-avoiding Permutations

Abstract

We consider permutations that avoid the pattern 1324. We give exact formulas for thenumber of reducible 1324-avoiding permutations and the number of {1324, 4132, 2413, 3241}-avoiding permutations. By studying the generating tree for all 1324-avoiding permutations,we obtain a recurrence formula for their number. A computer program provides data for thenumber of 1324-avoiding permutations of length up to 20.