Hook-length Formulas for Skew Shapes via Contour Integrals and Vertex Models Article Swipe
Greta Panova
,
Leonid Petrov
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.17842
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.17842
The number of standard Young tableaux of a skew shape $λ/μ$ can be computed as a sum over excited diagrams inside $λ$. Excited diagrams are in bijection with certain lozenge tilings, with flagged semistandard tableaux and also nonintersecting lattice paths inside $λ$. We give two new proofs of a multivariate generalization of this formula, which allow us to extend the setup beyond standard Young tableaux and the underlying Schur symmetric polynomials. The first proof uses multiple contour integrals. The second one interprets excited diagrams as configurations of a six-vertex model at a free fermion point, and derives the formula for the number of standard Young tableaux of a skew shape from the Yang-Baxter equation.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2409.17842
- https://arxiv.org/pdf/2409.17842
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4403796600
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4403796600Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2409.17842Digital Object Identifier
- Title
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Hook-length Formulas for Skew Shapes via Contour Integrals and Vertex ModelsWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-09-26Full publication date if available
- Authors
-
Greta Panova, Leonid PetrovList of authors in order
- Landing page
-
https://arxiv.org/abs/2409.17842Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2409.17842Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2409.17842Direct OA link when available
- Concepts
-
Skew, Hook, Vertex (graph theory), Mathematics, Combinatorics, Geometry, Computer science, Graph, Engineering, Structural engineering, TelecommunicationsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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