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 |