An operator formula for the number of halved monotone triangles with prescribed bottom row

DOI10.1016/j.jcta.2008.05.013zbMath1235.05010arXivmath/0702637OpenAlexW2095052675WikidataQ59196587 ScholiaQ59196587MaRDI QIDQ1024358

Ilse Fischer

Publication date: 17 June 2009

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702637

zbMATH Keywords

alternating sign matricesmonotone trianglesoperator formulas

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15)

Related Items (4)

Refined enumeration of symmetry classes of alternating sign matrices ⋮ Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity ⋮ Refined enumeration of halved monotone triangles and applications to vertically symmetric alternating sign trapezoids ⋮ Constant term formulas for refined enumerations of Gog and Magog trapezoids

Uses Software

• ROBBINS

Cites Work

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• Refined enumerations of some symmetry classes of alternating-sign matrices
• The number of monotone triangles with prescribed bottom row
• A new proof of the refined alternating sign matrix theorem
• Quantum Knizhnik-Zamolodchikov equation, totally symmetric self-complementary plane partitions, and alternating sign matrices
• Alternating sign matrices and descending plane partitions
• Odd symplectic groups
• Proof of the Macdonald conjecture
• Proof of the refined alternating sign matrix conjecture
• Symmetry classes of alternating-sign matrices under one roof
• Proof of the alternating sign matrix conjecture
• Quantum Knizhnik–Zamolodchikov equation: reflecting boundary conditions and combinatorics

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