As a matter of fact, Boole's algebraic manipulations can be regarded as derived rules arising from the following replacement rule, a nonuniform version of substitution. A=B D=C[⋯A⋯]D=C[⋯B⋯] This rule may be seen to codify Boole's practice and its doctrine. For he captur...
By the Murnaghan–Nakayama rule [11, Corollary 7.17.4],can be expressed in the basis of Schur polynomials as Observe that the coefficient ofin the expansion ofis. This is precisely the restricted row sum (ignoring the columns not in) of the character table of. These values need not always ...