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SpechtModule :: indexMonomial(YoungTableau,YoungTableau,PolynomialRing)

indexMonomial(YoungTableau,YoungTableau,PolynomialRing) -- a monomial that represents an index tableau

Synopsis

Description

The index monomial is used in the construction of higher Specht polynomials. To calculate the index monomial first the index tableau of S, i(S) is calculated. Then the monomial is calculated as xTi(S). This is a monomial with the variables as they appear in T with the exponents that appear in i(S).

i1 : R = QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing
i2 : p = new Partition from {2,2,1}

o2 = Partition{2, 2, 1}

o2 : Partition
i3 : S  = youngTableau(p,{0,2,1,3,4})

o3 = | 0 2 |
     | 1 3 |
     | 4 |

o3 : YoungTableau
i4 : T  = youngTableau(p,{0,1,2,3,4})

o4 = | 0 1 |
     | 2 3 |
     | 4 |

o4 : YoungTableau
i5 : ind = indexTableau(S)

o5 = | 0 1 |
     | 1 2 |
     | 3 |

o5 : YoungTableau
i6 : indexMonomial(S,T,R)

          2 3
o6 = x x x x
      1 2 3 4

o6 : R

See also