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- W1963809736 abstract "Noncrossing set partitions, nonnesting set partitions, Dyck paths, and rooted plane trees are four classes of Catalan objects which carry a notion of type. There exists a product formula which enumerates these objects according to type. We define a notion of ‘connectivity’ for these objects and prove an analogous product formula which counts connected objects by type. Our proof of this product formula is combinatorial and bijective. We extend this to a product formula which counts objects with a fixed type and number of connected components. We relate our product formulas to symmetric functions arising from parking functions. We close by presenting an alternative proof of our product formulas communicated to us by Christian Krattenthaler (2010) [7] which uses generating functions and Lagrange inversion." @default.
- W1963809736 created "2016-06-24" @default.
- W1963809736 creator A5016834944 @default.
- W1963809736 date "2011-02-01" @default.
- W1963809736 modified "2023-09-29" @default.
- W1963809736 title "Enumeration of connected Catalan objects by type" @default.
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- W1963809736 doi "https://doi.org/10.1016/j.ejc.2010.10.007" @default.
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