On the work performed by a transformation semigroup

East, James and McNamara, Peter J. (2011) On the work performed by a transformation semigroup. Australasian Journal of Combinatorics, 49 95-109.

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Author East, James
McNamara, Peter J.
Title On the work performed by a transformation semigroup
Journal name Australasian Journal of Combinatorics   Check publisher's open access policy
ISSN 1034-4942
2202-3518
Publication date 2011
Sub-type Article (original research)
Open Access Status
Volume 49
Start page 95
End page 109
Total pages 15
Place of publication Brisbane, QLD Australia
Publisher Centre for Discrete Mathematics and Computing
Language eng
Formatted abstract
A (partial) transformation α on the finite set {1,...,n} moves an element i of its domain a distance of |i − iα| units. The work w(α) performed by α is the sum of all of these distances. We derive formulae for the total work w(S) = α∈S w(α) performed by various semigroups S of (partial) transformations. One of our main results is the proof of a conjecture of Tim Lavers which states that the total work performed by the semigroup of all order-preserving functions on an n-element chain is equal to (n − 1)22n−3.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Fri, 17 Apr 2015, 16:56:30 EST by Kay Mackie on behalf of School of Mathematics & Physics