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A Problem in Partitions: Enumeration of Elements of a given Degree in the free commutative entropic cyclic Groupoid

Published online by Cambridge University Press:  20 January 2009

H. Minc
The University of British Columbia, Vancouver, Canada
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A groupoid is a set closed with respect to a binary operation. It is commutative and entropic if xy = yx and = xz.yw hold for all its elements. It is cyclic if it is generated by one element. Let x be the generator of the free commutative entropic cyclic groupoid . Then any element of can be written in the form xP where x1 = x and xQ+R = xQxR. Two indices P, Q are equal (called “concordant” in (3)) if and only if xP = xQ. The groupoid of these indices, the free additive commutative entropic logarithmetic (cf. (3)), is clearly isomorphic to .

Research Article
Copyright © Edinburgh Mathematical Society 1959



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