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Combinatorial Interpretations Of Generalizations Of Catalan Numbers And Ballot Numbers

2018

The super Catalan numbers T(m,n) = (2m)!(2n)!=2m!n!(m+n)! are integers which generalize the Catalan numbers. Since 1874, when Eugene Catalan discovered these numbers, many mathematicians have tried to find their combinatorial interpretation. This dissertation is dedicated to this open problem. In Chapter 1 we review known results on T (m,n) and their q-analog polynomials. In Chapter 2 we give a weighted interpretation for T(m,n) in terms of 2-Motzkin paths of length m+n2 and a reformulation of

doi:10.1184/r1/6715193
fatcat:m6kw3vswgnh7lh6ietpim4mh24