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Researchers proved that the q-Ehrhart series of a hyperplane slice of a cube is a rational function with an explicit denominator satisfying q-reciprocity, confirming a conjecture by Reiner and Rhoades. They also identified a generating set for the orbit harmonics ideal, yielding the Hilbert series...
Researchers proved that the q-Ehrhart series of a hyperplane slice of a cube is a rational function with an explicit denominator satisfying q-reciprocity, confirming a conjecture by Reiner and Rhoades. They also identified a generating set for the orbit harmonics ideal, yielding the Hilbert series...
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We prove that the $q$-Ehrhart series of a hyperplane slice of a cube is a rational function with an explicit denominator that satisfies $q$-reciprocity, confirming a conjecture of Reiner and Rhoades for these polytopes. To do this, we find a generating set for the orbit harmonics ideal, which also yields the...
This result advances the understanding of Ehrhart theory and combinatorial properties of polytopes, providing explicit algebraic structures related to hypersimplices. It confirms a long-standing conjecture, offering new tools for further research in algebraic combinatorics.
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