3 papers
math.CO2026
On separable permutations and three other pairs in the Schröder class
Juan B. Gil, Oscar A. Lopez, Michael D. Weiner
We study positional statistics for four families of pattern-avoiding permutations counted by the large Schröder numbers. Specifically, we focus on the pairs of patterns $\{2413,31…
math.CO2026
Rooted bicubic planar maps via Dyck paths
Juan B. Gil, Jackie N. Kaminski
We provide a combinatorial proof of Tutte's decomposition of rooted bicubic planar maps into 3-connected components. Motivated by the framework of Bell transformations, we establis…
math.CO2024
A positional statistic for 1324-avoiding permutations
Juan B. Gil, Oscar A. Lopez, Michael D. Weiner
We consider the class of permutations of size that avoid the pattern 1324 and examine the subset of elements for which ,…