It is quite noticeable than this word – “WLOG” (=Without Loss Of Generality) is strewn across the net and books …. This post shall convey its real meaning.
(1) If a function – is symmetric
If for some permutation – with
Since the function is symmetric,
Therefore , Proving,
Thus a pairwise order can be assumed in symmetric functions..
(2) If a function – is cyclic
Since the function is only cyclic , we only have –
We can either have –
$latex y \ge z,x$
Thus , proving ,
where is any cyclic permutation of with
P.S. Thanks to Tejs Mathias for making me understand this.