Geodesic
Pattern popularity in 132-avoiding permutations
Kate Rudolph1
1Massachusetts Institute of Technology
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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The popularity of a pattern $p$ is the total number of copies of $p$ within all permutations of a set. We address popularity in the set of $132$-avoidng permutations. Bóna showed that in this set, all other non-monotone length-$3$ patterns are equipopular, and proved equipopularity relations between some length-$k$ patterns of a specific form. We prove equipopularity relations between general length-$k$ patterns, based on the structure of their corresponding binary plane trees. Our result explains all equipopularity relations for patterns of length up to $7$, and we conjecture that it provides a complete classification of equipopularity in $132$-avoiding permutations.
DOI : 10.37236/2634
Classification : 05A05, 05A15, 05A19
Mots-clés : permutations, pattern-avoidance, pattern popularity, equipopular patterns, equipopularity relations

Kate Rudolph  1

1 Massachusetts Institute of Technology 
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Kate Rudolph. Pattern popularity in 132-avoiding permutations. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2634

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