Restricted Patience Sorting and Barred Pattern Avoidance

Details Restricted Patience Sorting and Barred Pattern Avoidance Restricted Patience Sorting and Barred Pattern Avoidance

2005-12-06

arxiv.org/abs/math/0512122v2

Mathematics

Combinatorics

12 pages, LaTeX, uses pstricks, needs fpsac.cls v2: final version of extended abstract for FPSAC'06

Scientific paper

Patience Sorting is a combinatorial algorithm that can be viewed as an iterated, non-recursive form of the Schensted Insertion Algorithm. In recent work the authors have shown that Patience Sorting provides an algorithmic description for permutations avoiding the barred (generalized) permutation pattern $3-\bar{1}-42$. Motivated by this and a recently formulated geometric form for Patience Sorting in terms of certain intersecting lattice paths, we study the related themes of restricted input and avoidance of similar barred permutation patterns. One such result is to characterize those permutations for which Patience Sorting is an invertible algorithm as the set of permutations simultaneously avoiding the barred patterns $3-\bar{1}-42$ and $3-\bar{1}-24$. We then enumerate this avoidance set, which involves convolved Fibonacci numbers.

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