A complete homogeneous symmetric polynomial 
is the sum of all monomials of total degree 
in 
variables, where 
is a nonnegative integer
and 
is a positive integer:
 |
where the indices are nonnegative integers and 
.
For example, 
and 
.
These are symmetric polynomials as well as
homogeneous polynomials.
The McLeod conjecture concerns ratios of complete homogeneous symmetric polynomials (Sra 2026, p. 1).
