The representation of the symmetric group on \(m\)-Tamari intervals
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Publication:2437563
DOI10.1016/j.aim.2013.07.014zbMath1283.05268OpenAlexW2142210784MaRDI QIDQ2437563
Mireille Bousquet-Mélou, Louis-François Préville-Ratelle, Guillaume Chapuy
Publication date: 3 March 2014
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.aim.2013.07.014
Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30)
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Cites Work
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- Hyperplane arrangements and diagonal harmonics
- The case \(k=2\) of the shuffle conjecture
- A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants
- The number of intervals in the \(m\)-Tamari lattices
- Intervals in Catalan lattices and realizers of triangulations
- Conjectures on the quotient ring by diagonal invariants
- Generating functions for generating trees
- Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
- Basic analytic combinatorics of directed lattice paths
- A polytope related to empirical distributions, plane trees, parking functions, and the associahedron
- A combinatorial formula for the character of the diagonal coinvariants
- A proof of the \(q,t\)-Catalan positivity conjecture
- Conjectured statistics for the \(q,t\)-Catalan numbers.
- A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
- Higher trivariate diagonal harmonics via generalized Tamari posets
- Combinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics
- Polynomial equations with one catalytic variable, algebraic series and map enumeration
- Problems of associativity: a simple proof for the lattice property of systems ordered by a semi-associative law
- A conjectured combinatorial formula for the Hilbert series for diagonal harmonics
- A problem of arrangements
- Two Parking Function Bijections: A Sharpening of the q,t-Catalan and Shröder Theorems
- A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path
- Walks with small steps in the quarter plane
- Hall–Littlewood Operators in the Theory of Parking Functions and Diagonal Harmonics
- Problèmes d'associativité: Une structure de treillis finis induite par une loi demi-associative
- Ballots and trees
- Generalized parking functions, tree inversions, and multicolored graphs
