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Seminar: The water capacity of Dyck paths
Speaker: Arnold Knopfmacher, University of the Witwatersrand, South Africa
Abstract: A Dyck path is a lattice path in the first quadrant with up steps (1,1) and down steps (1,-1) that starts and ends on the x-axis. We study the amount of water that would be retained in the valleys of the path if water was poured into the Dyck path shape from above. We extend the results to derive also the water capacity of Catalan words. These are words w1w2…wn of length n where w1=1 and w_{i+1} <= w_{i}+1, for 1 <= i <= n-1.
Keywords: Dyck Path, Water Capacity, Lattice Path Statistics