2021/07/09 by Sergi Elizalde, Elizalde, Sergi, Bruce E. Sagan +1
Agricultural and Biological Sciences · Computer Science · Mathematics · #05A05 #05A15 #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2107.04717
openalex publication_date 2021/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In their study of cyclic pattern containment, Domagalski et al. conjecture differential equations for the generating functions of circular permutations avoiding consecutive patterns of length 3. In this note, we prove and significantly generalize these conjectures. We show that, for every consecutive pattern σ beginning with 1, the bivariate generating function counting occurrences of σ in circular permutations can be obtained from the generating function counting occurrences of σ in (linear) permutations. This includes all the patterns for which the latter generating function is known.