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A presentation for the monoid of uniform block permutations

  • D. G. FitzGerald (a1)

Abstract

The monoid n of uniform block permutations is the factorisable inverse monoid which arises from the natural action of the symmetric group on the join semilattice of equivalences on an n-set; it has been described in the literature as the factorisable part of the dual symmetric inverse monoid. The present paper gives and proves correct a monoid presentation forn. The methods involved make use of a general criterion for a monoid generated by a group and an idempotent to be inverse, the structure of factorisable inverse monoids, and presentations of the symmetric group and the join semilattice of equivalences on an n-set.

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Copyright

References

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[1]Chen, S.Y. and Hsieh, S.C., ‘Factorizable inverse semigroups’, Semigroup Forum 8 (1974), 283297.
[2]FitzGerald, D.G. and Leech, J., ‘Dual symmetric inverse monoids and representation theory’, J. Austral. Math. Soc. Ser. A 64 (1998), 345367.
[3]Grillet, P.A., Semigroups: an introduction to the structure theory (Marcel Dekker, New York, 1995).
[4]Lawson, M.V., Inverse semigroups: the theory of partial symmetries (World Scientific, Singapore, 1998).
[5]Moore, E.H., ‘Concerning the abstract groups of order k! and ½k! holohedrically isomorphic with the symmetric and alternating substitution groups on k letters’, Proc. London Math. Soc. 28 (1897), 357366.
[6]Popova, L.M., ‘Defining relations in some semigroups of partial transformations of a finite set’, (in Russian), Uchenye Zap. Leningrad. Gos. Ped. Inst. 218 (1961), 191212.
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A presentation for the monoid of uniform block permutations

  • D. G. FitzGerald (a1)

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