A necessary and sufficient condition that ![[alpha^']](/images/equations/MuirheadsTheorem/Inline1.svg)
should be comparable with ![[alpha]](/images/equations/MuirheadsTheorem/Inline2.svg)
for all positive values
of the 
is that one of (
)
and (
)
should be majorized by the other. If 
, then
![[alpha^']<=[alpha],](/images/equations/MuirheadsTheorem/NumberedEquation1.svg) |
with equality only when (
) and (
) are identical or when all the 
are equal. See Hardy et al. (1988) for a definition
of notation.
Letters." Proc. Edinburgh Math. Soc. 21,
144-157, 1903.