2024/09/08 by Colin Defant, Defant, Colin, Mitchell Lee +1
Computer Science · #05A05 #05A18 #05A19 #46L53 #Advanced Algebra and Logic #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2409.05219
openalex publication_date 2024/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Defant found that the relationship between a sequence of (univariate) classical cumulants and the corresponding sequence of (univariate) free cumulants can be described combinatorially in terms of families of binary plane trees called troupes. Using a generalization of troupes that we call weighted troupes, we generalize this result to allow for multivariate cumulants. Our result also gives a combinatorial description of the corresponding Boolean cumulants. This allows us to answer a question of Defant regarding his troupe transform. We also provide explicit distributions whose cumulants correspond to some specific weighted troupes.