2021- Fall Symposium of Student Scholars

Project Title

t-Stack Sorting on the Permutahedron

Academic department under which the project should be listed

CSM - Mathematics

DR. JULIANNE VEGA

Andres R Vindas-Melendez, Mathematical Sciences Research Institute & Department of Mathematics at University of California Berkeley, avindas@msri.org

Disciplines

Algebraic Geometry | Discrete Mathematics and Combinatorics | Geometry and Topology | Number Theory | Other Mathematics | Theory and Algorithms

Abstract (300 words maximum)

In 1968, Knuth introduced the stack sorting algorithm which attempts to chronologically sort an inputted sequence, in our case a permutation. Using the stack sorting algorithm, we traverse the vertices and edges of the permutahedron. The n-permutahedron is the (n-1)-dimensional polytope generated by the convex hull of permutations of the first n natural numbers. We consider subpolytopes of the permutahedron arising from the convex hull of sequences generated by iterations of the stack sorting algorithm. For a particular family of subpolytopes, we determine their dimension and prove that they are simplices. We conjecture that this family of simplices has Ehrhart polynomials with coefficients in Pascal’s triangle.

Project Type

Oral Presentation (15-min time slots)

How will this be presented?

Yes, asynchronously via recorded video upload

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t-Stack Sorting on the Permutahedron

In 1968, Knuth introduced the stack sorting algorithm which attempts to chronologically sort an inputted sequence, in our case a permutation. Using the stack sorting algorithm, we traverse the vertices and edges of the permutahedron. The n-permutahedron is the (n-1)-dimensional polytope generated by the convex hull of permutations of the first n natural numbers. We consider subpolytopes of the permutahedron arising from the convex hull of sequences generated by iterations of the stack sorting algorithm. For a particular family of subpolytopes, we determine their dimension and prove that they are simplices. We conjecture that this family of simplices has Ehrhart polynomials with coefficients in Pascal’s triangle.