
Recent Posts
Recent Comments
Simon on How much it costs to raise a… aquazorcarson on How much it costs to raise a… Simon on How much it costs to raise a… aquazorcarson on Friendship is costly Erwin on Friendship is costly Archives
 November 2017
 October 2017
 August 2017
 July 2017
 June 2017
 October 2016
 September 2016
 July 2016
 June 2016
 May 2016
 March 2016
 July 2015
 May 2015
 March 2015
 February 2015
 January 2015
 November 2014
 October 2014
 June 2014
 March 2014
 February 2014
 December 2013
 November 2013
 October 2013
 August 2013
 July 2013
 May 2013
 April 2013
 March 2013
 January 2013
 September 2012
 January 2012
 December 2011
 September 2011
 August 2011
 July 2011
 June 2011
 April 2011
 March 2011
 February 2011
 January 2011
 November 2010
 October 2010
 September 2010
 July 2010
 June 2010
 May 2010
 April 2010
 March 2010
 February 2010
 January 2010
 December 2009
 October 2009
 September 2009
 August 2009
 July 2009
 June 2009
 May 2009
 April 2009
 March 2009
 February 2009
 January 2009
 October 2008
 September 2008
 July 2008
 June 2008
 May 2008
 April 2008
 March 2008
 February 2008
 January 2008
 October 2007
 September 2007
 August 2007
 July 2007
 April 2007
 March 2007
 February 2007
 December 2006
 November 2006
 October 2006
 September 2006
 August 2006
Categories
Meta
Monthly Archives: January 2011
Algebraic combinatorics lecture 6: RS(K), Dual RSK, and analytic definition of Schur functions
First we have an easy result Proposition 1 where is the number of SSYT of shape and type . Proof: We know that Equating coefficient of both sides, we get on LHS and on RHS. Thus we also have . … Continue reading
Posted in algebraic combinatorics, Uncategorized
Leave a comment
Algebraic combinatorics lecture 5: RSK algorithm
First we describe the Schensted algorithm, which associates to each permutation two Young tableaux of the same shape but possibly different types; it consists of bumping numbers into a greedy patience sorting procedure. In the first step we write down. … Continue reading
Posted in algebraic combinatorics, Uncategorized
Tagged combinatorics, Diaconis, RSK algorithm, symmetric functions
Leave a comment
Algebraic combinatorics Lecture 4: patience sorting, symmetry of schur functions and Kostka numbers
Recall the definition of skew Young tableaux and their Schur functions and . When , we get the usual Schur functions .The reason we consider skew tableaux is they are related to skew characters of to be discussed later. the … Continue reading
Posted in algebraic combinatorics, Uncategorized
Tagged card shuffling, combinatorics, Diaconis
Leave a comment
Graphical inference model: lecture 4. Max product algorithm and group testing
Max product is algorithm is closely related to the sum product algorithm, in that it uses partial marginals to compute the total marginal. But the objective is to find the mode of a distribution, i.e., . It does that by … Continue reading
Gurvits’ inequality and proof of Van der Waerden’s conjecture
Today I went to Don Knuth’s talk on some recent spectacular progress made in the problem of computing permanents. The talk is motivated and mainly based on a recent article in the American Math Monthly called “On Leonid Gurvits’s proof … Continue reading
Algebraic combinatorics Lecture 3
First it is useful to have the Hall inner product on , the space of all symmetric functions in infinitely many variables. It is defined by To show it’s symmetric, we check it on the basis . Then it follows … Continue reading
Posted in algebraic combinatorics, Uncategorized
Tagged combinatorics, Diaconis, symmetric functions
Leave a comment
Graphical inference model lecture 2
The indexing and bookkeeping of notations in this class have always been a nightmare to me. I try my best to state things correctly. Whenever possible I copy directly from Andrea’s notes. The moral of today’s lesson is that trees … Continue reading