Timeline for Simple proof that certain walks in the plane don't intersect

6 events

when toggle format	what		by	license	comment
Apr 17 at 6:04	answer	added	Fedor Petrov		timeline score: 6
Apr 16 at 7:23	comment	added	Fedor Petrov		Equivalent reformulation: if $A=\{(x,y)\in \mathbb{Z}^2: n\geqslant x\geqslant y\geqslant 1\}$, consider all functions $f\colon A\to \mathbb{Z}_{\geqslant 0}$ which are non-strictly increasing both in $x$ and in $y$ (this is in obvious bijection with more common objects like skew semistandard Young tableaux), and sum up the monomials $p^{\sum_{i=1}^n f(i,i)}$ over all such functions. The sum equals $(1-p)^{-n}(1-p^2)^{-{n\choose 2}}$.
Apr 15 at 20:17	comment	added	Philippe Nadeau		Sure, I meant that a bijective proof of Littlewood identity would certainly explain why the sum was not needed in the first place.
Apr 15 at 14:19	comment	added	Richard Stanley		@PhilippeNadeau: ideally there would be no sums in the proof, since none appear in the answer.
Apr 15 at 6:31	comment	added	Philippe Nadeau		From the linked slides it seems such a proof would be a corollary of a 'simple proof' of Littlewood identity for the sum of Schur functions. I suppose there's some variant of RSK that proves those ?
Apr 15 at 3:12	history	asked	Richard Stanley	CC BY-SA 4.0