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Extensive categories and the size of an orbit

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Ernie Manes

It is well known how to compute the number of orbits of a group action. A
related problem, apparently not in the literature, is to determine the number
of elements in an orbit. The theory that addresses this question leads to
orbital extensive categories and to combinatorial aspects of such categories.

Keywords:
extensive category, Burnside-Frobenius lemma, conjugacy class of subgroups

2010 MSC:
05A99, 18B99, 20B05

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 17, pp 599-619.

Published 2015-05-04.

http://www.tac.mta.ca/tac/volumes/30/17/30-17.pdf

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