Finite difference calculus for alternating permutations

Abstract

The finite difference equation system introduced by Christiane Poupard in the study of tangent trees is reinterpreted in the alternating permutation environment. It makes it possible to make a joint study of both tangent and secant trees and calculate the generating polynomial for alternating permutations by a new statistic, referred to as being the greater neighbour of the maximum.

Keywords::

• difference equation system
• Poupard triangle
• tangent numbers
• secant numbers
• alternating permutations
• strictly ordered binary trees

Acknowledgement

The authors thank the referee for his careful reading and his knowledgeable remarks.

Notes

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