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Peer-reviewedCC BY 4.0The Electronic Journal of Combinatorics

A Generalization of RSK to d-Complete Posets

  • Son Nguyen
  • Joseph Vulakh
  • Dora Woodruff
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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 the first purely combinatorial proof of the hook length formula for d-complete posets. Our approach is to define a generalization of the Robinson-Schensted-Knuth bijection for d-complete posets, which may be of independent interest.

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Cite

BibTeXRIS
BibTeX
@article{nguyen2026generalization,
  title = {{A Generalization of RSK to d-Complete Posets}},
  author = {Son Nguyen and Joseph Vulakh and Dora Woodruff},
  journal = {The Electronic Journal of Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.37236/15257},
  url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Generalization of RSK to d-Complete Posets
AU  - Son Nguyen
AU  - Joseph Vulakh
AU  - Dora Woodruff
PY  - 2026
DA  - 2026/10/09
JO  - The Electronic Journal of Combinatorics
DO  - 10.37236/15257
UR  - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p1
AB  - 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 the first purely combinatorial proof of the hook length formula for d-complete posets. Our approach is to define a generalization of the Robinson-Schensted-Knuth bijection for d-complete posets, which may be of independent interest.
SN  - 1077-8926
ER  -