Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
Title: Solving Prellberg and Mortimer's conjecture - bijection(s)
between Motzkin paths and triangular walks
Speaker: | Julien Courtiel |
Affiliation: | Université de Caen |
Zoom: | Contact Karen Yeats |
Abstract:
In these difficult times, what we need to feel better is some colorful and elegant bijections.
This talk introduces the work we did with Andrew Elvey-Price (Tours, France) and Irène Marcovici (Nancy, France). Together we answered an open question from Mortimer and Prellberg, asking for a bijection between a family of walks inside a bounded triangular domain (think about a large equilateral triangle subdivided in several smaller equilateral triangles) and the famous Motzkin paths, but which have bounded height.
The used techniques for the proof are quite elementary, and seem to be robust. Indeed, in addition to solving Mortimer and Prellberg's conjecture, our approach enabled us to find a new surprising bijection between 3D-walks constrained inside a pyramid and some 2D-walks in a squared grid.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.