Connectivity patterns in loop percolation. I: The rationality phenomenon and constant term identities

DOI10.1007/s00220-014-2001-5zbMath1296.82030arXiv1303.6341OpenAlexW2166243741MaRDI QIDQ2509631

Dan Romik

Publication date: 29 July 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.6341

zbMATH Keywords

square latticeloop percolation

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) PDEs in connection with quantum mechanics (35Q40) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items

Fully packed loop configurations: polynomiality and nested arches ⋮ The toggle group, homomesy, and the Razumov-Stroganov correspondence ⋮ Connectivity patterns in loop percolation. I: The rationality phenomenon and constant term identities ⋮ Short proof of the ASM theorem avoiding the six-vertex model ⋮ Unnamed Item ⋮ Enumeration of alternating sign triangles using a constant term approach

Uses Software

• GoodDyson
• GuessRat
• ROBBINS

Cites Work

• Proof of the Razumov-Stroganov conjecture
• Deformed Kazhdan-Lusztig elements and Macdonald polynomials
• Quantum Knizhnik-Zamolodchikov equation, totally symmetric self-complementary plane partitions, and alternating sign matrices
• On the doubly refined enumeration of alternating sign matrices and totally symmetric self-complementary plane partitions
• Izergin-Korepin determinant at a third root of unity
• Alternating sign matrices and descending plane partitions
• Determinant identities
• Plane partitions. V: The TSSCPP conjecture
• Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions
• A large dihedral symmetry of the set of alternating sign matrices
• Around the Razumov-Stroganov conjecture: proof of a multi-parameter sum rule
• One-arm exponent for critical 2D percolation
• On the counting of fully packed loop configurations: some new conjectures
• Proof of the alternating sign matrix conjecture
• Quantum incompressibility and Razumov Stroganov type conjectures
• Enumeration of symmetry classes of alternating sign matrices and characters of classical groups
• Connectivity patterns in loop percolation. I: The rationality phenomenon and constant term identities
• Loops, matchings and alternating-sign matrices
• Combinatorial nature of the ground-state vector of the \(\mathrm{O}(1)\) loop model
• The quantum symmetricXXZchain at Δ = -½, alternating-sign matrices and plane partitions
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• Statistical Theory of the Energy Levels of Complex Systems. I
• On some ground state components of the O(1) loop model
• Disturbing the Dyson Conjecture (in a GOOD Way)
• Proof of a Conjecture by Dyson in the Statistical Theory of Energy Levels
• Percolation
• Temperley Lieb stochastic processes
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• Proof of a Conjecture by Dyson
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