The Combinatorics of Triangulations of Products of Two Simplices
Name
yao-yyao1-phd-math-2026-thesis.pdf
Size
1.9 MB
Format
Adobe PDF
Checksum (MD5)
715868d21e73c6de63d038fedeea0246
Author(s)
Yao, Yuan
Advisor(s)
Postnikov, Alexander
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
We study the combinatorial structure of triangulations of the Cartesian product of two standard simplices, a seemingly simple object that is deeply connected to many objects spanning across polyhedral geometry, tropical geometry, topology, algebraic geometry, and matroid theory. In the first part, we extend our current understanding in the case where one of the two simplices has dimension two or three. In the second part, we establish several new cryptomorphisms between triangulations and related objects, addressing some gaps in the current literature. Finally, we study a generalization where the triangulated polytope is a sub-polytope of the product of two simplices, and generalize the related combinatorial characterizations accordingly.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Copyright retained by author(s)
Persistent DSpace Link
