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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
Twisted Associative Algebras and Shuffle Algebras 133
an S-polynomial of g
1
and g
2
; the common term cancels, since both g
1
and g
2
are monic.
Example 4.5.1.2. Consider the shuffle monomial 321 T
X
(1)(3). This
monomial forms two different overlaps with itself: we have
4321 = µ
{2,3,4},{1}
(321, 1) = µ
{4},{1,2,3}
(1, 321)
and
54321 = µ
{3,4,5},{1,2}
(321, 21) = µ
{4,5},{1,2,3}
(21, 321).
In this case, there is one small common multiple of weight 4, and one small
common multiple of weight 5. However, the situation might be very different,
as the shuffle monomial 312 T
X
(1)(3) demonstrates. This monomial does
not have an overlap of weight 4 with itself: if the permutation ...
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Publisher Resources

ISBN: 9781482248579