19 Aug
2014
19 Aug
'14
9:48 p.m.
Sorry, one additional question: 3. how constraining is associativity, in the sense of reducing the number of different operators? E.g., commutativity cuts out nearly half of the degrees of freedom; what % of the degrees of freedom does associativity cut out ? At 06:02 PM 8/19/2014, Henry Baker wrote:
I'm interested in binary operations on a finite set S that are associative, period; no other constraints.
1. Are there "fast" methods for checking associativity given the operation table?
2. Can all such associative operations be emulated "efficiently" using an isomorphism in which the operation is matrix multiplication (not just over standard rings, but extended like Knuth & the APL language do) ?
(RCS knows why I'm asking this question.)