Meet and join within the lattice of set partitions.
Canfield, Rodney E. (2001)
The Electronic Journal of Combinatorics [electronic only]
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Canfield, Rodney E. (2001)
The Electronic Journal of Combinatorics [electronic only]
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Athanasiadis, Christos A. (1998)
The Electronic Journal of Combinatorics [electronic only]
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David Wang (2014)
Open Mathematics
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Generalizing Reiner’s notion of set partitions of type B n, we define colored B n-partitions by coloring the elements in and not in the zero-block respectively. Considering the generating function of colored B n-partitions, we get the exact formulas for the expectation and variance of the number of non-zero-blocks in a random colored B n-partition. We find an asymptotic expression of the total number of colored B n-partitions up to an error of O(n −1/2log7/2 n], and prove that the centralized...
Callan, David (2008)
Journal of Integer Sequences [electronic only]
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Knopfmacher, A., Odlyzko, A.M., Pittel, B., Richmond, L.B., Stark, D., Szekeres, G., Wormald, N.C. (1999)
The Electronic Journal of Combinatorics [electronic only]
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Griffiths, Martin, Mező, István (2010)
Journal of Integer Sequences [electronic only]
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Klazar, Martin (2005)
The Electronic Journal of Combinatorics [electronic only]
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Pittel, Boris (2000)
The Electronic Journal of Combinatorics [electronic only]
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Václav Havel (1966)
Časopis pro pěstování matematiky
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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,...
Bousquet-Mélou, Mireille, Xin, Guoce (2005)
Séminaire Lotharingien de Combinatoire [electronic only]
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