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math.CO2026
Motzkin paths, 321-avoiding permutations, and standard Young tableaux with rows of equal parity
Ryan Amaral, Ryan J. Amaral, Juan B. Gil +1
Motzkin paths of length and standard Young tableaux (SYT) with cells and at most three rows are both counted by the Motzkin numbers, and many bijections between them are kn…
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.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 $\{2413,314…