A continuous family of partition statistics equidistributed with length

DOI10.1016/j.jcta.2008.07.001zbMath1188.05012OpenAlexW2039139573MaRDI QIDQ1003648

Gregory S. Warrington, Nicholas A. Loehr

Publication date: 4 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.jcta.2008.07.001

zbMATH Keywords

armmultigraphpartitionbijectionlattice pathEulerian tourleg

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17)

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Cites Work

• Unnamed Item
• On the homology of the Hilbert scheme of points in the plane
• Cylindrical lattice walks and the Loehr-Warrington \(10^{n}\) conjecture
• \(t,q\)-Catalan numbers and the Hilbert scheme.
• A combinatorial formula for the character of the diagonal coinvariants
• On a cell decomposition of the Hilbert scheme of points in the plane.
• Conjectured statistics for the higher \(q,t\)-Catalan sequences
• A proof of the \(q,t\)-Catalan positivity conjecture
• Conjectured statistics for the \(q,t\)-Catalan numbers.
• Some theorems on actions of algebraic groups
• A positivity result in the theory of Macdonald polynomials
• The Family G_Tof Graded Artinian Quotients ofk[x,y of Given Hilbert Function]