@MISC{Stasheff96thepre-history, author = {Jim Stasheff and Jim Stasheff}, title = {The Pre-History Of Operads}, year = {1996} }

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Abstract

ae ae ae ae ae ae ae ae B B B B B B B B B B \Theta \Theta \Theta \Theta \Theta \Theta \Theta \Theta \Theta Z Z Z Z Z Z Z Z (ab)(cd) a(b(cd)) ((ab)c)d a((bc)d) (a(bc))d While I continued this work as a student in Oxford, Frank Adams visited and discussed his work with Mac Lane on PACTs and PROPs. With a key idea from Adams, I created the polytopes now known as associahedra [11]. The name is due to Gil Kalai, a geometric combinatorialist [6, 5]. The associahedron K n can be described now as a convex polytope with one vertex for each way of associating n ordered variables, that is, ways of inserting parentheses in a meaningful way in a word of n letters. For n = 5, here is a portrait I copy (literally) from Masahico Saito. From a slighly different perspective, the 6-fold cyclic symmetry is more manifest, as in this portrait I learned from John Harer a very few years ago. (It also appears in Kap