@MISC{Labri_right-cancellabilityof, author = {Philippe Duchon Labri}, title = {Right-Cancellability of a Family of Operations on Binary Trees}, year = {} }

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Abstract

Introduction The product a#b,wherea and b are positive integers, can be expressed as the sum of b terms, each being equal to a. Similarly, a b can be expressed as the product of b factors, each being equal to a. This basically works well because the sum and product operations for integers are associative; to push this process one level further (i.e. define a new operation by iterating exponentiation), one needs to decides on how to order the operations in the expression a # a # ####a (where # is the exponentiation operation). One solution is to always perform the operations in a fixed order, usually right-to-left (see Blackley and Borosh [1] or Knuth [2]). Another, richer solution is to use the structure of a binary tree to set the order, and use binary trees instead of integer