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,

with

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 –

$latex y \ge z,x$

Let with

with

with

Thus , proving ,

where is any cyclic permutation of with

P.S. Thanks to Tejs Mathias for making me understand this.

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can someone please tell why atleast one latex code doesnt get converted every post!!!!????