====== Rigoberto Flórez (The Citadel) ======

====== Dyck Paths and Fibonacci Numbers ======

===== Abstract for the Combinatorics Seminar 2016 June 28 =====

A //Dyck path// is a path in the first quadrant of the planar integral lattice with only northeast and southeast steps, beginning at the origin and ending on the x-axis. It is //non-decreasing// if its valleys (local minima) are non-decreasing from left to right. Leandro Junes, Eva Czabarka, and I discovered a relationship between Fibonacci numbers and the depths of the valleys from the preceding peaks (called their "weights") in a non-decreasing Dyck path. I discuss two ways to count these paths.


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