IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Counting non-decreasing Dyck paths

  • Nov. 21, 2014
  • 2:30 p.m.
  • LeConte 312

Abstract

A Dyck word is a word in the letters X and Y with as many X's as Y's and in which no initial segment has more Y 's than X's. Each Dyck word gives rise to a path (Dyck). These are paths connecting points using north-east steps and south-east steps in a grid (in the xy-plane) formed with non-negative integers. Dyck paths start at the origin and end on the x-axis.

A Dyck path P is non-decreasing if the y-coordinates of the local minima (valleys) of the path P form a non-decreasing sequence. Using power series in several variables we count the number of local maxima (peaks), the pyramid weights. We also discuss how to extend the basic power series to obtain some other statistics on non-decreasing Dyck paths.

This is joint work with E. Czabarka and L. Junes.

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