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math.CO2025
Ehrhart Theory over Abelian Group Rings
Robert Davis, Jesús A. De Loera, Alexey Garber +3
We introduce a unified framework for Ehrhart theory in which lattice point enumerators take coefficients in an Abelian group ring, encoding substantially richer algebraic data than…
math.CO2025
An arithmetic measure of width for convex bodies
Jesús A. De Loera, Brittney Marsters, Christopher O'Neill
We introduce the arithmetic width of a convex body, defined as the number of distinct values a linear functional attains on the lattice points within the body. Arithmetic width ref…