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The set of Dyck paths of length $2n$ inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order.
Two element lattice permutation numbers and their q q -generalization
Leonard Carlitz and John Riordan · 1964
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Théorie Géométrique des Polynômes Eulériens
Dominique Foata and Marcel-P. Schützenberger · 1970
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Problem: q q -analog of the lagrange expansion
Leonard Carlitz · 1974
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The Theory of Partitions
George E. Andrews · 1976
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An introduction to Ramanujan’s “lost” notebook
George E. Andrews · 1979
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Combinatorial aspects of continued fractions
Philippe Flajolet · 1980
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On inversions and cycles in permutations
Paul H. Edelman · 1987
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The Editor’s Corner: n n Coins in a Fountain
Andrew M. Odlyzko and Herbert S. Wilf · 1988
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On the structure of the lattice of noncrossing partitions
Rodica Simion and Daniel Ullman · 1991
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Some properties of crossings and partitions
Philippe Biane · 1997
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New Euler-Mahonian statistics on permutations and words
Robert J. Clarke, Einar Steingrímsson, and Jiang Zeng · 1997
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Non-crossing partitions for classical reflection groups
Victor Reiner · 1997
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Deformation of chains via a local symmetric group action
Patricia Hersh · 1999
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Enumerative Combinatorics. Vol. 2
Richard P. Stanley · 1999
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An area-to-inv bijection between Dyck paths and 312-avoiding permutations
Jason Bandlow and Kendra Killpatrick · 2001
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Catalan continued fractions and increasing subsequences in permutations
Petter Brändén, Anders Claesson, and Einar Steingrímsson · 2002
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Coxeter cones and their h h -vectors
John R. Stembridge · 2008
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Generalized Noncrossing Partitions and Combinatorics of Coxeter groups
Drew Armstrong · 2009
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Catalan structures and catalan pairs
Stefano Bilotta, Filippo Disanto, Renzo Pinzani, and Simone Rinaldi · 2010
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Eulerian quasisymmetric functions
John Shareshian and Michelle L. Wachs · 2010
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A uniform bijection between nonnesting and noncrossing partitions
Drew Armstrong, Christian Stump, and Hugh Thomas · 2011
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On γ \gamma -vectors satisfying the Kruskal-Katona inequalities
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Sign-graded posets, unimodality of W W -polynomials and the Charney-Davis conjecture
Petter Brändén · 2004
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Real root conjecture fails for five- and higher-dimensional spheres
Światosław R. Gal · 2005
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The q q , t t -Catalan Numbers and the Space of Diagonal Harmonics
James Haglund · 2008
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Faces of generalized permutohedra
Alex Postnikov, Victor Reiner, and Lauren Williams · 2008
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Meanders in a cayley graph
H. Tracy Hall
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Eran Nevo and T. Kyle Petersen · 2011
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The γ \gamma -vector of a barycentric subdivision
Eran Nevo, T. Kyle Petersen, and Bridget Eileen Tenner · 2011
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A decomposition of the shard intersection order on the symmetric group
T. Kyle Petersen · 2011
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The sorting index
T. Kyle Petersen · 2011
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More bijective Catalan combinatorics on permutations and colored permutations
Christian Stump · 2012
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