Displaying similar documents to “Nonhomogeneous parking functions and noncrossing partitions.”

Compositions of n as alternating sequences of weakly increasing and strictly decreasing partitions

Aubrey Blecher, Charlotte Brennan, Toufik Mansour (2012)

Open Mathematics

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Compositions and partitions of positive integers are often studied in separate frameworks where partitions are given by q-series generating functions and compositions exhibiting specific patterns are designated by generating functions for these patterns. Here, we view compositions as alternating sequences of weakly increasing and strictly decreasing partitions (i.e. alternating blocks). We obtain generating functions for the number of such partitions in terms of the size of the composition,...

Symmetric partitions and pairings

Ferenc Oravecz (2000)

Colloquium Mathematicae

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The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.