With your host…Alan Quebec
Group theory Orbits and counting
Coding theory Potpourri
$100 $100 $100 $100$200 $200 $200 $200$300 $300 $300 $300$400 $400 $400 $400
$500 $500 $500 $500
The four group axioms
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ClosureAssociativity
IdentityInverses
A group with 11 elements is this kind of group
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Cyclic
The easiest way to tell if a subset of G is a subgroup
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Check that if x, y are elements of H, then so is
xy-1
Why S5 cannot have a subgroup of order 7
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Lagrange’s Theorem
There are this many elements of order 13 in
C13
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12 (1 has order 1)
The difference between Gx and Gx(Not just the names of the terms, but their meanings)
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Gx is the orbit containing x; Gx is the stabilizer of x
The size of an orbit if G = S4
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4
The number of ways to color the edges of a pentagon red, green,
and blue
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The number of ways to place colored pie slices into a Trivial Pursuit game piece like
the one below, if only the orange and yellow pieces can be used
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The number of ways to color the edges of a pentagon red, green, and blue where 2 edges are green and 2
edges are blue
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Coefficient of rb2g2 is
The number of errors that this code can correct for:00000, 01100, 00111, 11001
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0 (minimum distance is 2)
The length of a codeword in the linear code given by the
associated matrix
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7
The maximum number of codewords in a code of length 7 that can correct for one
error
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16, since
The number of codewords in the linear code given by the
associated matrix
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24 = 16
This is the smallest linear code that contains the codewords
001, 110
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000, 100, 011, 111(code must be a group)
These three sets are all rings
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A ring that is not a field has this distinguishing
characteristic
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Not all nonzero elements have multiplicative inverses
This is an example of an invertible power series where all coefficients are nonzero and the coefficient of
is 10
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Any matching power series that has a invertible constant term
The parity (even or odd) of the permutation (12345)
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Even; decomposition into transpositions is (12)(23)(34)(45)
The order of the permutation(12)(345)
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lcm(2, 3) = 6