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.
Academic department under which the project should be listed
CSM - Mathematics
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Primary Investigator (PI) Name
DR. JULIANNE VEGA
Additional Faculty
Andres R Vindas-Melendez, Mathematical Sciences Research Institute & Department of Mathematics at University of California Berkeley, avindas@msri.org
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.