Advances and Applications in Discrete Mathematics
Volume 7, Issue 2, Pages 95 - 108
(April 2011)
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WORDS OVER A WEAK ASSOCIATIVE MAGMA
Jean Marcel Pallo
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To this aim, we use a bijection
between words and binary trees. This leads to consider a restricted rotation.
Nontrivial equivalence classes of words with n open and n close
parentheses are enumerated by the sequence
where
is the nth
Fibonacci number. The rotation ordering induces a lattice structure on these
equivalence classes.