Sinai Robins

collaborators

2 papers

math.CO2026

Half-open integer parallelepipeds and polytope Dedekind sums

Sinai Robins, André Rosenbaum Coelho

We study the Ehrhart theory of half-open $d$ -dimensional integer parallelepipeds $Π$ . Although the lattice-point count $t Π \cap Z^{d}$ is known to be simply $\vol Πt^d$ for positive…

math.CO2026

Ehrhart quasi-polynomials via Barnes polynomials and discrete moments of parallelepipeds

Sinai Robins

We give novel explicit formulas for the Ehrhart quasi-polynomials of any rational polytope $P$ , in terms of Barnes polynomials and discrete moments of half-open parallelepipeds. Th…