Parity statistics on restricted permutations and the Catalan--Schett
polynomials
Parity statistics on restricted permutations and the Catalan--Schett
polynomials
Motivated by Kitaev and Zhang's recent work on non-overlapping ascents in stack-sortable permutations and Dumont's permutation interpretation of the Jacobi elliptic functions, we investigate some parity statistics on restricted permutations. Some new related bijections are constructed and two refinements of the generating function for descents over $321$-avoiding permutations due to …