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Simply generated trees, B‐series and Wigner processes
Author(s) -
Mazza Christian
Publication year - 2004
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20024
Subject(s) - series (stratigraphy) , mathematics , class (philosophy) , tree (set theory) , limiting , generating function , product (mathematics) , pure mathematics , factorial , discrete mathematics , combinatorics , computer science , mathematical analysis , geometry , mechanical engineering , paleontology , artificial intelligence , engineering , biology
We consider simply generated trees, like rooted plane trees, and consider the problem of computing generating functions of so‐called bare functionals, like the tree factorial, using B‐series from Butcher's theory. We exhibit a special class of functionals from probability theory: the associated generating functions can be seen as limiting traces of product of semi‐circular elements. © 2004 Wiley Periodicals, Inc. Random Struct. Alg. 2004