• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.529-541
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• 2013

We study 132 avoiding permutations that also avoid $(2r+1)(2r+2){\cdots}12$ but contain $(2r-1)(2r){\cdots}12$ pattern. We find an identity between the number of these permutations and the Narayana number. We also present relations between 132 avoiding permutations and polygon dissections. Finally, a generalization of these permutations is obtained.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.189-198
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• 2007

We have defined a bijective map from certain set of coinstacks onto the permutations avoiding 132-pattern and give an algorithm that finds a corresponding permutation from a given coin-stack. We also list several open problems which are similar as a CS-partition problem.