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

## 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 $x_T^{i(S)}$. 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