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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 171
an S-polynomial of g
1
and g
2
; the common term cancels, since both g
1
and g
2
are monic.
Example 5.5.1.2. Let us consider the shuffle associative operad Ass
f
dis-
cussed in Example 5.3.4.3, and the following two of its six defining relations:
g
1
=
1 3
a
2
a
2 3
1
b
a
and g
2
=
1 3
b
2
a
1 2
a
3
b
.
Let us consider, for the purpose of this example, the following ordering: to
compare two shuffle tree monomials T and T
0
of the same arity, we compare
the number of internal vertices labelled by b, then if those numbers are the
same, compare T and T
0
using the order gpathpermlex for b a. In this case,
the leading monomials of the elements above
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Publisher Resources

ISBN: 9781482248579