Enumeration of Indices of Given Altitude and Degree
- 1 June 1960
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 12 (1) , 1-5
- https://doi.org/10.1017/s0013091500024986
Abstract
This note is a sequel to the article by Mine (2) on the same problem.I described in (1) a notation for indices of powers in non-associative algebra, defined the degree † and altitude of a power or index, and observed that powers can be represented by bifurcating root-trees. For example, the power xx.x is denoted x2 + 1, with index 2 + 1, and is represented by the tree ; the degree (the number of factors, or free knots in the tree) is 3, and the altitude (the height of the tree) is 2. Multiplication being non-commutative or commutative, one maintains or ignores the distinction between left and right in the tree.Keywords
This publication has 2 references indexed in Scilit:
- Enumeration of Indices of given Altitude and PotencyProceedings of the Edinburgh Mathematical Society, 1959
- XV.—On Non-Associative CombinationsProceedings of the Royal Society of Edinburgh, 1940