Combinatorial results for the symmetric inverse semigroup

A. Laradji; A. Umar

doi:10.1007/s00233-007-0732-8

Combinatorial results for the symmetric inverse semigroup

A. Laradji^*, A. Umar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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'.

Original language	English
Pages (from-to)	221-236
Number of pages	16
Journal	Semigroup Forum
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s00233-007-0732-8
Publication status	Published - Sept 2007
Externally published	Yes

Keywords

Derangement
Exponential generating function
Full transformation
Laguerre polynomial
Nilpotent
Ordinary generating function
Partial one-one transformation
Partial transformation
Permutation
Semigroup

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s00233-007-0732-8

Cite this

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AU - Umar, A.

PY - 2007/9

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AB - 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'.

KW - Derangement

KW - Exponential generating function

KW - Full transformation

KW - Laguerre polynomial

KW - Nilpotent

KW - Ordinary generating function

KW - Partial one-one transformation

KW - Partial transformation

KW - Permutation

KW - Semigroup

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M3 - Article

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SP - 221

EP - 236

JO - Semigroup Forum

JF - Semigroup Forum

IS - 1

ER -

Combinatorial results for the symmetric inverse semigroup

Abstract

Keywords

ASJC Scopus subject areas

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