Catalan Numbers Day - May 14

Happy Catalan Numbers Day! Catalan numbers are a sequence of numbers that represent the counts of several mathematical concepts. They're named after Eugene Charles Catalan , a French-Belgian mathematician who worked on number theory and combinatorics . One of the things Catalan numbers count are the number of Dyck words, which are words consisting of X's and Y's which: Consist of an equal number of X's and Y's, And where all beginning sub-words have their number of X's greater than or equal to their number of Y's. For example, XYXY is a Dyck word because XYX, XY, and X are all beginning sub-words where there are at least as many X's as Y's. But XYYX is not a Dyck word because XYY is a beginning sub-word where there are more Y's than X's. Note that if you substitute "(" for X and ")" for Y, Dyck words constitute a valid sequence for arithmetic or regular expressions. Here are the smallest Dyck words. This video provides...