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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
226 Algebraic Operads: An Algorithmic Companion
Definition 7.2.3.5 (Action of permutations on orders). Let σ S
k
be any
permutation of 1, . . . , k and let be any monomial order. The monomial order
σ
is defined in terms of the action of S
k
permuting the coordinates of vectors
in N
k
. That is, we first set
σ · [e
1
, . . . , e
i
, . . . , e
k
] = [e
σ(1)
, . . . , e
σ(i)
, . . . , e
σ(k)
],
and then we define
σ
in terms of by
v
σ
w ⇐⇒ σ
1
· v σ
1
· w.
(To cancel the σ on we need to apply σ
1
.) That is, given v = [e
1
, . . . , e
k
]
and w = [f
1
, . . . , f
k
] with v 6= w, let i be the least index satisfying the inequal-
ity e
σ
1
(i)
6= f
σ
1
(i)
. Then v w if and only if
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Publisher Resources

ISBN: 9781482248579