2025/11/27 by Sano, Kaoru
#05A05 #05A15 #05A16 #05A19 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2511.22015
Fix a strong rectangulation pattern P of size L. We show that the growth constant of the class of strong rectangulations avoiding P is strictly smaller than Λ=27/2, the growth constant for all strong rectangulations. More precisely, forbidding any such P yields a pattern-uniform exponential drop of at least Λ- 1/Λ3L-1. Consequently, the proportion of P-avoiding rectangulations among all rectangulations tends to zero as n→ ∞. This is the first result on the uniform drop of exponential growth for pattern-avoiding rectangulations. The proof utilizes the standard correspondence with leftmost history quadrant walks, along with a pattern-insertion scheme that controls the radius of convergence of the associated generating functions, thereby establishing the first uniform exponential upper bound for rectangulation classes defined by geometric avoidance.