Geodesic
Surprising symmetries in objects counted by Catalan numbers
Miklós Bóna1
1University of Florida
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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We prove that the total number $S_{n,132}(q)$ of copies of the pattern $q$ in all 132-avoiding permutations of length $n$ is the same for $q=231$, $q=312$, or $q=213$. We provide a combinatorial proof for this unexpected threefold symmetry. We then significantly generalize this result by proving a large family of non-trivial equalities of the type $S_{n,132}(q)=S_{n,132}(q')$.
DOI : 10.37236/2060
Classification : 05A05, 05A15
Mots-clés : permutations, patterns, plane trees, bijection

Miklós Bóna  1

1 University of Florida 
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     author = {Mikl\'os B\'ona},
     title = {Surprising symmetries in objects counted by {Catalan} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/2060},
     zbl = {1243.05006},
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Miklós Bóna. Surprising symmetries in objects counted by Catalan numbers. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/2060

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