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Combinatorial Results for the Symmetric Inverse Semigroup

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Abstract

In this note we obtain and discuss formulae for the number of partial one-one transformations (of an n-element set) of height (equivalently, width) r and having exactly k fixed points. Moreover, we consider a generalization of the 'Hat Problem' or 'Probleme des Rencontres'.

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Authors and Affiliations

  1. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

    A. Laradji & A. Umar

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  1. A. Laradji
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  2. A. Umar
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Correspondence to A. Laradji or A. Umar.

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Laradji, A., Umar, A. Combinatorial Results for the Symmetric Inverse Semigroup. Semigroup Forum 75, 221–236 (2007). https://doi.org/10.1007/s00233-007-0732-8

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  • DOI: https://doi.org/10.1007/s00233-007-0732-8

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