DisCoMath Seminar: Some Enumerations on Non-decreasing Dyck Paths
Some Enumerations on Non-decreasing Dyck Paths
Dr. Rigoberto Flórez
Associate Professor
Department of Mathematics and Computer Science
The Citadel
Abstract:
A Dyck path is a lattice path in the first quadrant of the xy-plane that starts at the origin and ends on the x-axis. It consists of the same number of North-East (U) and South-East (D) steps.
A pyramid is a sub-path of the form UnDn. A valley is a sub-path of the form DU. The height of a valley is the y-coordinate of its lowest point. A Dyck path is called non-decreasing if the heights of its valleys form a non-decreasing sequence from left to right. In this talk, we count several aspects of non-decreasing Dyck paths. We count, for example, the number and weight of pyramids and numbers of primitive paths. In the end of the talk we introduce the concept of symmetric pyramids and count them. Throughout the talk, we give connections (bijective relations) between non-decreasing Dyck paths with other objects of the combinatorics. Some examples are, words, trees, polyominoes. This is a joint work with Eva Czabarka, José L. Ramírez, and Leandro Junes.
Speaker Bio:
Dr. Flórez is an Associate Professor in the Department of Mathematical Sciences at the Citadel, South Carolina. He earned his Ph.D. in Mathematics from Binghamton University (SUNY). His research is in combinatorics, especially graphs and algebraically representable matroids. He is also interested in elementary number theory and enumerative combinatorics. Rigo likes working research projects with undergraduate and graduate students. His students have presented their research in local and national conferences and they have won awards doing the same. He is one of the founders of Carolina Math Seminar.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
Keep up with DisCoMath Seminars on the DisCoMathS webpage.
Event Snapshot
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This is an RIT Only Event
Interpreter Requested?
No