Combinatorial proof of a recurrence for the Catalan numbers - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T01:31:47Z http://mathoverflow.net/feeds/question/34246 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/34246/combinatorial-proof-of-a-recurrence-for-the-catalan-numbers Combinatorial proof of a recurrence for the Catalan numbers Thomas Li 2010-08-02T11:27:36Z 2011-12-14T17:18:14Z <p>I would like to ask whether there is a combinatorial proof of the following recurrence relation for Catalan numbers: $$C_{n+1}=\frac{4n+2}{n+2} C_n.$$</p> <p>Thanks!~</p> http://mathoverflow.net/questions/34246/combinatorial-proof-of-a-recurrence-for-the-catalan-numbers/34259#34259 Answer by Pietro Majer for Combinatorial proof of a recurrence for the Catalan numbers Pietro Majer 2010-08-02T13:16:21Z 2010-08-02T13:16:21Z <p>What you are asking is reported as fourth proof in the wiki article for the formula of the Catalan numbers: <a href="http://en.wikipedia.org/wiki/Catalan_number#Fourth_proof" rel="nofollow">http://en.wikipedia.org/wiki/Catalan_number#Fourth_proof</a></p> http://mathoverflow.net/questions/34246/combinatorial-proof-of-a-recurrence-for-the-catalan-numbers/36364#36364 Answer by Hashem sazegar for Combinatorial proof of a recurrence for the Catalan numbers Hashem sazegar 2010-08-22T08:36:47Z 2010-08-22T08:45:03Z <p>these papers can you help:</p> <p><a href="http://www.geometer.org/mathcircles/catalan.pdf" rel="nofollow">http://www.geometer.org/mathcircles/catalan.pdf</a></p> <p><a href="http://docs.google.com/viewer?a=v&amp;q=cache:IPxobgy1BIcJ:www.math.ucsd.edu/~gptesler/184a/catalan_f08-handout.pdf+catalan+number&amp;hl=en&amp;pid=bl&amp;srcid=ADGEESiPvWTzNFP0Z5y7CRCrf83opSMRhhCMCNSirJYnBnk_4KnLIIxe6rvj8K2DO39epTp5rZjHszeLloOot62UjlqayX96E9kw-Uw6PJ-eVbE6-rXkH-ZtxBxv6YwJrl9U9-zbJQ5F&amp;sig=AHIEtbTXYSM6J_QnxsOMWpD1_vmFbYe7yg" rel="nofollow">http://docs.google.com/viewer?a=v&amp;q=cache:IPxobgy1BIcJ:www.math.ucsd.edu/~gptesler/184a/catalan_f08-handout.pdf+catalan+number&amp;hl=en&amp;pid=bl&amp;srcid=ADGEESiPvWTzNFP0Z5y7CRCrf83opSMRhhCMCNSirJYnBnk_4KnLIIxe6rvj8K2DO39epTp5rZjHszeLloOot62UjlqayX96E9kw-Uw6PJ-eVbE6-rXkH-ZtxBxv6YwJrl9U9-zbJQ5F&amp;sig=AHIEtbTXYSM6J_QnxsOMWpD1_vmFbYe7yg</a></p>