3,585 research outputs found
Combinatorics of r-Dyck paths, r-Parking functions, and the r-Tamari lattices
This paper's aim is to present recent combinatorial considerations on r-Dyck
paths, r-Parking functions, and the r-Tamari lattices. Giving a better
understanding of the combinatorics of these objects has become important in
view of their (conjectural) role in the description of the graded character of
the Sn-modules of bivariate and trivariate diagonal coinvariant spaces for the
symmetric group.Comment: 36 pages, 12 figure
Transitive factorizations of permutations and geometry
We give an account of our work on transitive factorizations of permutations.
The work has had impact upon other areas of mathematics such as the enumeration
of graph embeddings, random matrices, branched covers, and the moduli spaces of
curves. Aspects of these seemingly unrelated areas are seen to be related in a
unifying view from the perspective of algebraic combinatorics. At several
points this work has intertwined with Richard Stanley's in significant ways.Comment: 12 pages, dedicated to Richard Stanley on the occasion of his 70th
birthda
A Survey of Alternating Permutations
This survey of alternating permutations and Euler numbers includes
refinements of Euler numbers, other occurrences of Euler numbers, longest
alternating subsequences, umbral enumeration of classes of alternating
permutations, and the cd-index of the symmetric group.Comment: 32 pages, 7 figure
Enumeration of Standard Young Tableaux
A survey paper, to appear as a chapter in a forthcoming Handbook on
Enumeration.Comment: 65 pages, small correction
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