The Catalan numbers show up in a diverse variety of counting problems. In this note we give yet another characterization of the Catalan number C(n). It is characterized as the dimension of a certain space of multilinear polynomials by exhibiting a basis.
Catalan numbers, stack-sortable permutations, permutations acting on polynomials.
GÜLOĞLU, İSMAİL Ş. and KOÇ, CEMAL
"Stack-Sortable Permutations and Polynomials,"
Turkish Journal of Mathematics: Vol. 33:
1, Article 1.
Available at: https://journals.tubitak.gov.tr/math/vol33/iss1/1