A generalization of RSK to d-complete posets

2025/08/19 by Nguyen, Son, Vulakh, Joseph, Woodruff, Dora
#05A19 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.13988

Abstract

The hook length formula for d-complete posets expresses the number of linear extensions of a d-complete poset P in terms of hooks of P. It generalizes the usual hook length formula for standard Young tableaux, as well as hook length formulas for shifted Young tableaux and trees. We give a new proof of the hook length formula for d-complete posets which is elementary and purely combinatorial. Our approach is to define a generalization of the Robinson-Schensted-Knuth bijection for d-complete posets, which may be of independent interest.

Citations

• RSK via local transformations
• Hook, line and sinker: a bijective proof of the skew shifted hook-length formula
• Hook length property of d-complete posets via q-integrals
• d-Complete posets: local structural axioms, properties, and equivalent definitions
• A bijective proof of the hook-length formula for skew shapes
• d-Complete Posets Generalize Young Diagrams for the Jeu de Taquin\n Property
• Towards a Littlewood-Richardson rule for Kac-Moody homogeneous spaces

Related

• The weighted hook length formula III: Shifted tableaux
• Playing jeu de taquin on d-complete posets
• Hook length property of d-complete posets via q-integrals
• Counting linear extensions of posets with determinants of hook lengths
• d-Complete posets: local structural axioms, properties, and equivalent definitions