2021/03/18 by Phan Thuan, Do, Phan Thuan, Thi Thu Huong Tran +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algorithms and Data Compression #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2103.10357
openalex publication_date 2021/03/18 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28
We prove the equidistribution of several multistatistics over some classes of permutations avoiding a 3-length pattern. We deduce the equidistribution, on the one hand of inv and foze" statistics, and on the other hand that of maj and makl statistics, over these classes of pattern avoiding permutations. Here inv and maj are the celebrated Mahonian statistics, foze" is one of the statistics defined in terms of generalized patterns in the 2000 pioneering paper of Babson and Steingrímsson, and makl is one of the statistics defined by Clarke, Steingrímsson and Zeng in 1997. These results solve several conjectures posed by Amini in 2018.