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Algebraic Operads
book

Algebraic Operads

by Murray R. Bremner, Vladimir Dotsenko
April 2016
Intermediate to advanced content levelIntermediate to advanced
383 pages
11h 46m
English
Chapman and Hall/CRC
Content preview from Algebraic Operads
Symmetric Operads and Shuffle Operads 151
Let us describe an explicit construction of the free shuffle operad with a
given set of generators.
Definition 5.3.1.2 (Shuffle tree monomial). Let X = {X(n)}
n1
be
a reduced operation alphabet. A shuffle tree monomial in X is a triple
T = (τ, x, n), where
τ is a planar rooted tree all of whose endpoints are leaves;
x is a labelling of all internal vertices of τ by elements of X; each vertex
v must have a label x
v
X(|Parent
1
(v)|);
n is a numbering of leaves of τ by integers 1, . . . , |Leaves(τ)| satisfying
the following local increasing condition stated as follows.
Any numbering n of leaves induces a numbering
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Publisher Resources

ISBN: 9781482248579