2025/01/20 by Asinowski, Andrei, Polley, Michaela A. · 1 citation
#05A05 #05A15 #05A19 #05B45 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.11781
We initiate a systematic study of pattern avoidance in rectangulations. We give a formal definition of such patterns and investigate rectangulations that avoid \top-like patterns - the pattern \top and its rotations. For every L ⊆ \\top, \vdash, \bot, \dashv \ we enumerate L-avoiding rectangulations, both weak and strong. In particular, we show \top-avoiding weak rectangulations are enumerated by Catalan numbers and construct bijections to several Catalan structures. Then, we prove that \top-avoiding strong rectangulations are in bijection with several classes of inversion sequences, among them I(010,101,120,201) and I(011,201) - which leads to a solution of the conjecture that these classes are Wilf-equivalent. Finally, we show that \\top, \bot\-avoiding strong rectangulations are in bijection with recently introduced rushed Dyck paths.