Annals of Combinatorics

, 15:51

The X-Class and Almost-Increasing Permutations

Authors

    • Department of MathematicsDartmouth College
Article

DOI: 10.1007/s00026-011-0082-9

Cite this article as:
Elizalde, S. Ann. Comb. (2011) 15: 51. doi:10.1007/s00026-011-0082-9

Abstract

In this paper we give a bijection between the class of permutations that can be drawn on an X-shape and a certain set of permutations that appears in Knuth [4] in connection to sorting algorithms. A natural generalization of this set leads us to the definition of almost-increasing permutations, which is a one-parameter family of permutations that can be characterized in terms of forbidden patterns. We find generating functions for almost-increasing permutations by using their cycle structure to map them to colored Motzkin paths. We also give refined enumerations with respect to the number of cycles, fixed points, excedances, and inversions.

Mathematics Subject Classification

05A0505A15

Keywords

cycle diagrampattern-avoiding permutationpicture classX-class

Copyright information

© Springer Basel AG 2011