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math.MG2018
Spherical tetrahedra with rational volume, and spherical Pythagorean triples
Alexander Kolpakov, Sinai Robins
We study spherical tetrahedra with rational dihedral angles and rational volumes. Such tetrahedra occur in the Rational Simplex Conjecture by Cheeger and Simons, and we supply vast…
math.CO2018
Simple proofs and expressions for the restricted partition function and its polynomial part
S. Robins, C. Vignat
In this note, we provide a simple derivation of expressions for the restricted partition function and its polynomial part. Our proof relies on elementary algebra on rational functi…
math.CO2018
Cubic graphs, their Ehrhart quasi-polynomials, and a scissors congruence phenomenon
Cristina G. Fernandes, José C. de Pina, Jorge Luis Ramírez Alfonsín +1
The scissors congruence conjecture for the unimodular group is an analogue of Hilbert's third problem, for the equidecomposability of polytopes. Liu and Osserman studied the Ehrhar…