1,351 research outputs found
New identities in dendriform algebras
Dendriform structures arise naturally in algebraic combinatorics (where they
allow, for example, the splitting of the shuffle product into two pieces) and
through Rota-Baxter algebra structures (the latter appear, among others, in
differential systems and in the renormalization process of pQFT). We prove new
combinatorial identities in dendriform dialgebras that appear to be strongly
related to classical phenomena, such as the combinatorics of Lyndon words,
rewriting rules in Lie algebras, or the fine structure of the
Malvenuto-Reutenauer algebra. One of these identities is an abstract
noncommutative, dendriform, generalization of the Bohnenblust-Spitzer identity
and of an identity involving iterated Chen integrals due to C.S. Lam.Comment: 16 pages, LaTeX. Concrete examples and applications adde
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