group action

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Related to Transitive group: Faithful Group Action
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In [Borie and Thiery(2011)], the authors calculate the secondary invariants of the 61st transitive group over 14 variables whose cardinality is 50803200.
We chose to use the database of all transitive groups of degree [less than or equal to] 30 [Hulpke(2005)] available in Sage through the system GAP [GAP(1997)].
This table displays the statistics for transitive groups of degree 5.
The following figure plots Ratio in terms of [absolute value of G] for transitive groups on at most 9 variables.
Recently Sun Sun (2006) proved that for functions that are invariant under some transitive group action the block sensitivity is at least n1/3 and they gave an example of a function that has block sensitivity O([n.
G](n, k) for some transitive group G and some k [not equal to] 0.
n] [right arrow] {0,1} be a non-constant Boolean function invariant under a transitive group G.