56 citations · 226 across the 41 of their papers we have counts for
4 papers · 1 filter
A Pick-type theorem for halfway-lattice polygons
Charlene Chu, Yael Karshon
Given a polygon in the plane with vertices on lattice points, Pick's theorem expresses its area A in terms of the number I of lattice points in its interior and the number B of lat…
Revisiting Tietze-Nakajima - Local and Global Convexity for Maps
Yael Karshon, Christina Bjorndahl
A theorem of Tietze and Nakamija, from 1928, asserts that if a subset X of R^n is closed, connected, and locally convex, then it is convex. We give an analogous "local to global co…
Exact Euler Maclaurin formulas for simple lattice polytopes
Yael Karshon, Shlomo Sternberg, Jonathan Weitsman
Euler Maclaurin formulas for a polytope express the sum of the values of a function over the lattice points in the polytope in terms of integrals of the function and its derivative…
Euler Maclaurin with remainder for a simple integral polytope
Yael Karshon, Shlomo Sternberg, Jonathan Weitsman
We give an Euler Maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope. This formula is proved by ele…