Promotion and Evacuation

2008/06/28 by Richard P. Stanley, Stanley, Richard P. · 6 citations
Mathematics · #06A07 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:06A07

paper · pdf · doi:10.48550/arxiv.0806.4717

28 pages, 6 figures. Minor corrections and additional references

arxiv created 2008/07/21 · arxiv updated 2009/12/01

Abstract

Promotion and evacuation are bijections on the set of linear extensions of a finite poset first defined by Schutzenberger. This paper surveys the basic properties of these two operations and discusses some generalizations.

Cited by

• Orbits of toric promotion on bridge sums
• Evacuation of rectangular standard Young tableaux corresponds to reflection of \mathfraksl_n webs
• Promotion permutations and the Robinson--Schensted correspondence
• Promotion digraphs
• Cylindric growth diagrams, walks in simplices, and exclusion processes
• Interval-closed set rowmotion and homomesy on products of two chains

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• Promotion Sorting
• Promotion and evacuation on standard Young tableaux of rectangle and staircase shape
• On Promotion and Quasi-tangled Labelings of Posets
• K-promotion on m-packed labelings of posets
• Counting linear extensions of restricted posets