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Combinatorics of Nilpotents in Symmetric Inverse Semigroups
Olexandr Ganyushkin1and Volodymyr Mazorchuk2
1Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, 64, Volodymyrska St., 01033, Kyiv, Ukraine
2Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden
Annals of Combinatorics 8 (2) p.161-175 June, 2004
AMS Subject Classification: 05A15, 20M18, 20M20, 05A19
We show how several famous combinatorial sequences appear in the context of nilpotent elements of the full symmetric inverse semigroup ISn. These sequences appear either as cardinalities of certain nilpotent subsemigroups or as the numbers of special nilpotent elements and include the Lah numbers, the Bell numbers, the Stirling numbers of the second kind, the binomial coefficients and the Catalan numbers.
Keywords: cardinality, nilpotent element, symmetric inverse semigroup, Catalan numbers, cross-section


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