Abstract
Indices of the free logarithmetic correspond to bifurcating root-trees (cf.(4)), to Evans' non-associative numbers (3) and to Etherington's partitive numbers (2). The free commutative logarithmetic is the homomorph of f determined by the congruence relation P + Q ∼ Q + P. Formulæ for aδ and pα, i.e. the numbers of indices of of a given potency* δ and the number of indices of a given altitude α respectively, were given by Etherington (1), who also gave corresponding formulæ for commutative indices of . Other enumeration formulæ are contained in (5).
Publisher
Cambridge University Press (CUP)
Reference5 articles.
1. Index polynomials and bifurcating root-trees;Mine;Proc. Roy Soc. Edin.,1957
2. XV.—On Non-Associative Combinations
3. Nonassociative Number Theory
4. The free commutative entropic logarithmetic;Mine;Proc. Roy. Soc. Edin.,1959
5. Non-associative arithmetics;Etherington;Proc. Roy. Soc. Edin.,1949
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