Sweeping up zeta

zbMath1384.05161MaRDI QIDQ5916014

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Publication date: 20 April 2018

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: http://www.mat.univie.ac.at/~slc/wpapers/FPSAC2017/10%20Thomas%20Williams.html

zbMATH Keywords

affine Weyl groupssweep mapzeta maprational Catalan combinatorics

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Symmetric functions and generalizations (05E05) Representations of finite symmetric groups (20C30) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (11)

Combinatorics of the zeta map on rational Dyck paths ⋮ Irreducible components of minuscule affine Deligne-Lusztig varieties ⋮ An area-depth symmetric \(q, t\)-Catalan polynomial ⋮ Advances in the Theory of Cores and Simultaneous Core Partitions ⋮ Rational Dyck paths in the non relatively prime case ⋮ Dinv and area ⋮ Rational Shi tableaux and the skew length statistic ⋮ Sweeping up zeta ⋮ Sweeping up zeta ⋮ From Anderson to zeta ⋮ Unnamed Item

Cites Work

• Rational parking functions and Catalan numbers
• Combinatorics of the zeta map on rational Dyck paths
• Cyclic sieving and rational Catalan theory
• Rational associahedra and noncrossing partitions
• Sweep maps: a continuous family of sorting algorithms
• Inverting the rational sweep map
• A proof of the \(q,t\)-Catalan positivity conjecture
• A Schröder generalization of Haglund's statistic on Catalan paths
• Conjectured statistics for the \(q,t\)-Catalan numbers.
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• Combinatorics of certain higher \(q, t\)-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula
• Cyclic symmetry of the scaled simplex
• Compactified Jacobians and \(q,t\)-Catalan numbers. II
• Affine permutations and rational slope parking functions
• 𝑎𝑑-nilpotent 𝔟-ideals in 𝔰𝔩(𝔫) having a fixed class of nilpotence: combinatorics and enumeration
• Rational Shi tableaux and the skew length statistic
• Sweeping up zeta

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