Annals of Combinatorics

, 15:51 | Cite as

The X-Class and Almost-Increasing Permutations



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

05A05 05A15 


cycle diagram pattern-avoiding permutation picture class X-class 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA

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