2021/02/27 by Matteo Cervetti, Cervetti, Matteo
Agricultural and Biological Sciences · Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2103.00246
openalex publication_date 2021/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we continue the study of permutations avoiding the vincular pattern 1-32-4 by constructing a generating tree with a single label for these permutations. This construction finally provides a clearer explanation of why a certain recursive formula found by Callan actually counts these permutations, insofar as this formula was originally obtained only as a consequence of a very intricated bijection with a certain class of ordered rooted trees. This responds to a theoretical issue already raised by Duchi, Guerrini and Rinaldi. As a byproduct, we also obtain an algorithm to generate all these permutations and we refine their enumeration according to a simple statistic, which is the number of right-to-left maxima to the right of 1.