D]) consists in iterating their duplication theorems until their variables are nearly equal and then expanding in a series of elementary symmetric functions of the small differences between the variables.
Because the function is symmetric in the Z's, it can be expanded in elementary symmetric functions [E.
The j-th elementary symmetric function evaluated at [alpha], denoted [e.
We will show that the indices of certain "critical" elementary symmetric functions determine the remaining elementary symmetric function values.
What is the profile, if any, that corresponds to the sequence of six elementary symmetric function values [e.
Ruskey, Counting Strings with Given Elementary Symmetric Function Evaluations I: Strings over zp with p prime, SIAM Journal on Discrete Mathematics, 17 (2004) 675-685.
Ruskey, Counting Strings with Given Elementary Symmetric Function Evaluations II: Circular Strings, SIAM Journal on Discrete Mathematics, 18 (2004) 71-82.
Our initial interest in the elementary symmetric functions stems from the counting of degree n monic irreducible polynomials over finite fields with prescribed coefficients for [x.
Furthermore, the elementary symmetric functions are homogeneous so
The Littlewood-Richardson rule is a well-known procedure to calculate the product of two Schur functions, such as two elementary symmetric functions (see Macdonald (1995)).