Hypercubic billiard word: Difference between revisions
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where |''u''|<sub>''x''<sub>''i''</sub></sub> is the number of occurrences of the letter ''x''<sub>''i''</sub> in the word ''u''. Is it the case that for all ''r'' ≥ 1, all ''r''-ary billiard circular words (''r'' − 1)-balanced? (The answer is known to be "yes" for ''r'' = 1, 2.) | where |''u''|<sub>''x''<sub>''i''</sub></sub> is the number of occurrences of the letter ''x''<sub>''i''</sub> in the word ''u''. Is it the case that for all ''r'' ≥ 1, all ''r''-ary billiard circular words (''r'' − 1)-balanced? (The answer is known to be "yes" for ''r'' = 1, 2.) | ||
2. Must ternary billiard scales have maximum variety at most 4, the MV4 ones being exactly the ones of balance 2? Does billiardness impose a simple relationship between arity, maximum variety and balance? | 2. Must ternary billiard scales have maximum variety at most 4, the MV4 ones being exactly the ones of balance 2? Does billiardness impose a simple, deterministic relationship between arity, maximum variety and balance? | ||
== See also == | == See also == | ||