Abstract
The asymptotic distributions of the order of elements in alternating semigroups and in partial transformation semigroups are obtained and shown to coincide with that for the symmetric semigroup.
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References
J. Baillieul, Green’s relations in finite function semigroups, Aequationes Mathematicae, 1 (1972), 22–27.
C. D. Bass and K. H. Kim, Combinatorial properties of partial transformation semigroups, 1971, unpublished.
J. Dénes, Connections between transformation semigroups and graphs; in Theory of Graphs (Internat. Sympos., Rome, 1966), 93-101. Gordon and Beach, N. Y., 1967.
J. Dénes, On transformations, transformation-semigroups and groups; in Theory of Graphs, Proceedings of the Colloquium held at Tihany, Hungary, September 1966, 65–75. Academic Press, New York, 1968.
J. Dénes, Some combinatorial properties of transformations and their connection with the theory of graphs, J. Combinatorial Theory, 9 (1969), 108–116.
J. Dénes, Leképezések és leképezés félcsoportok, I, Magyar Tudományos Akadémia Matematikai Fizikai Osztájának Közleményei, 19 (1969), 247–269.
J. Dénes, On graph representation of semigroups, Proceedings of the Calgary International Conference on Combinatorial Structures and their Applications, 55-57. Edited by Richard Guy et al., Gordon and Beach, N. Y., 1970.
J. Dénes, P. Erdős and P. Turán, On some statistical properties of the alternating group of degree n, Enseignement Math., 2, 15 (1969), 89–99.
P. Erdős and P. Turán, On some problems of a statistical group theory. I., Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 4 (1965), 175–186.
P. Erdős and P. Turán, On some problems of a statistical group theory, II, Acta Math. Acad. Sci. Hungar., 18(1967), 151–163.
P. Erdős and P. Turán, On some problems of a statistical group theory. III, Acta Math. Acad. Sci. Hungar., 18 (1967), 309–320.
P. Erdős and P. Turán, On some problems of a statistical group theory. IV., Acta Math. Acad. Sci. Hungar., 19 (1968), 413–435.
B. Harris, The asymptotic distribution of the order of elements in symmetric semigroups, J. Combinatorial Theory Ser. A, 15 (1973), 66–74.
B. Harris and L. Schoenfeld, A composition theorem for the enumeration of certain subsets of the symmetric semigroup, in “Graph Theory and its Applications”, B. Harris, Ed., Academic Press, New York, 1970.
J. M. Howie, The subsemigroup generated by the idempotents of a full transformation semigroup, J. London Math. Soc., 41 (1966), 707–716.
N. Ito, A theorem on the alternating group, Math. Japonica, 2 (1951), 59–60.
K. H. Kim and J. Dénes, Boolean Matrix Theory and Applications, Unpublished Book Manuscript.
O. Ore, Some remarks on commutators, Proc. Amer. Math. Soc., 2 (1951), 307–314.
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© 1983 Springer Basel AG
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Harris, B. (1983). The asymptotic distribution of the order of elements in alternating semigroups and in partial transformation semigroups. In: Erdős, P., Alpár, L., Halász, G., Sárközy, A. (eds) Studies in Pure Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5438-2_26
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DOI: https://doi.org/10.1007/978-3-0348-5438-2_26
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