The q-Ehrhart Polynomials of Right Angle Simplices
Florence Lam
Department of Mathematics
Faculty Supervisor: Matthias Beck
My master’s thesis is related to Ehrhart theory, a subject focused on enumerating lattice points within polytopes. The main object in this theory is the Ehrhart polynomial L_P(t), which counts the integer points contained in the t^th dilate of an integral convex polytope P of dimension d. A surprising result in Ehrhart theory is that if P= ∆ is a right-angle simplex, then its Ehrhart polynomial L∆(t) contains Fourier-Dedekind sums. My research extends this to the q-analogue of the Ehrhart polynomial. More specifically, I am investigating the q-Ehrhart polynomials for right-angle simplices with pairwise relatively prime vertices, a case not yet discussed in the literature.