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 poly nominal by exhibiting a basis. | !"# $ % &$! ( ) * * #+ , , - . * / , / 0 1 * *2 . +)#, * , * - 2 / 0 * 3 * 1 ( ) * * #+ , 3 , #*, * 1 * ,. 1 # ) ) * . )0* # ), +0 4 + *2 + , , ( ) * * #+ , , $, +) . # *, . # *, *2 * . )0* $ # ), !" # $ # $ ! % & % % # $ ( ( % % ) # $ # $ & % * % + % # $# $ # $ # $ # $# $ # $ % ! 5 6758 6 7(9
