Difference between revisions of "Relations"
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| − | (x⊙y)⊙z=x⊙(y⊙z) | + | |
| + | How many of the nn2 binary operations are associative? | ||
| + | (x⊙y)⊙z=x⊙(y⊙z) | ||
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| + | https://mathoverflow.net/questions/110211/how-many-binary-operations-are-associative | ||
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| + | for n=2, exactly half of the 24=16 binary operations are associative. | ||
| + | But for n=3, only 113 of the 39=19,683 binary operations are associative, a count I do not trust, because it seems so much smaller than I anticipated. | ||
| + | It is difficult to count among the four billion (4,294,967,296) binary operations for n=4.) the OEIS sequence A023814. The n=4 number I couldn't easily compute is 3492. | ||
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| + | I would be interested in the asymptotic growth rate. Surely this is all well known...? Thanks for pointers! | ||
| + | Update. Following MSE link provided by Darij, I reached (via Gerry Myerson's pointer) | ||
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| + | http://oeis.org/search?q=1%2C2%2C3%2C6%2C11%2C23%2C47%2C106%2C235&language=english&go=Search | ||
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| + | Is the Ratio of Associative Binary Operations to All Binary Operations on a Set of n Elements Generally Small? | ||
Latest revision as of 18:17, 27 January 2021
How many of the nn2 binary operations are associative? (x⊙y)⊙z=x⊙(y⊙z) https://mathoverflow.net/questions/110211/how-many-binary-operations-are-associative for n=2, exactly half of the 24=16 binary operations are associative. But for n=3, only 113 of the 39=19,683 binary operations are associative, a count I do not trust, because it seems so much smaller than I anticipated. It is difficult to count among the four billion (4,294,967,296) binary operations for n=4.) the OEIS sequence A023814. The n=4 number I couldn't easily compute is 3492. I would be interested in the asymptotic growth rate. Surely this is all well known...? Thanks for pointers! Update. Following MSE link provided by Darij, I reached (via Gerry Myerson's pointer) http://oeis.org/search?q=1%2C2%2C3%2C6%2C11%2C23%2C47%2C106%2C235&language=english&go=Search Is the Ratio of Associative Binary Operations to All Binary Operations on a Set of n Elements Generally Small?
