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diff --git a/posts/2013-06-01-q-robinson-schensted-paper.md b/posts/2013-06-01-q-robinson-schensted-paper.md deleted file mode 100644 index 657412d..0000000 --- a/posts/2013-06-01-q-robinson-schensted-paper.md +++ /dev/null @@ -1,31 +0,0 @@ ---- -template: oldpost -title: A \(q\)-weighted Robinson-Schensted algorithm -date: 2013-06-01 -comments: true -tags: RS, \(q\)-Whittaker_functions, Macdonald_polynomials -archive: false ---- -In [this paper](https://projecteuclid.org/euclid.ejp/1465064320) with [Neil](http://www.bristol.ac.uk/maths/people/neil-m-oconnell/) we construct a \\(q\\)-version of the Robinson-Schensted -algorithm with column insertion. Like the [usual RS -correspondence](http://en.wikipedia.org/wiki/Robinson–Schensted_correspondence) -with column insertion, this algorithm could take words as input. Unlike -the usual RS algorithm, the output is a set of weighted pairs of -semistandard and standard Young tableaux \\((P,Q)\\) with the same -shape. The weights are rational functions of indeterminant \\(q\\). - -If \\(q\\in\[0,1\]\\), the algorithm can be considered as a randomised -RS algorithm, with 0 and 1 being two interesting cases. When -\\(q\\to0\\), it is reduced to the latter usual RS algorithm; while -when \\(q\\to1\\) with proper scaling it should scale to directed random -polymer model in [(O'Connell 2012)](http://arxiv.org/abs/0910.0069). -When the input word \\(w\\) is a random walk: - -\\begin{align\*}\\mathbb -P(w=v)=\\prod\_{i=1}^na\_{v\_i},\\qquad\\sum\_ja\_j=1\\end{align\*} - -the shape of output evolves as a Markov chain with kernel related to -\\(q\\)-Whittaker functions, which are Macdonald functions when -\\(t=0\\) with a factor. - - |