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With your host…Alan Quebec
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Group theoryOrbits 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
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The four group axioms
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ClosureAssociativity
IdentityInverses
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A group with 11 elements is this kind of group
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Cyclic
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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
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Why S5 cannot have a subgroup of order 7
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Lagrange’s Theorem
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There are this many elements of order 13 in
C13
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12 (1 has order 1)
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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
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The size of an orbit if G = S4
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4
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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
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The number of errors that this code can correct for:00000, 01100, 00111, 11001
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0 (minimum distance is 2)
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The length of a codeword in the linear code given by the
associated matrix
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7
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The maximum number of codewords in a code of length 7 that can correct for one
error
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16, since
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The number of codewords in the linear code given by the
associated matrix
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24 = 16
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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)
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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
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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
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The parity (even or odd) of the permutation (12345)
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Even; decomposition into transpositions is (12)(23)(34)(45)
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The order of the permutation(12)(345)
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lcm(2, 3) = 6