Fence complexes are associated to positroid varieties, shown to be balls with matching Ehrhart and Hilbert polynomials, and positroid varieties degenerate to reduced unions of toric varieties corresponding to the complexes.
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Proves if-and-only-if equivalences for toric ring normality and quadratic toric ideal generation between anti-blocking lattice polytopes and their unconditional reflections, plus a graph-theoretic characterization of quadratic symmetric stable set ideals.
Gorenstein simplices with the given h*-polynomial are classified up to unimodular equivalence by strict divisor chains in the divisor lattice of v, yielding an explicit counting formula.
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Fence Complexes and Toric Degenerations of Positroid Varieties
Fence complexes are associated to positroid varieties, shown to be balls with matching Ehrhart and Hilbert polynomials, and positroid varieties degenerate to reduced unions of toric varieties corresponding to the complexes.
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Algebraic aspects of unconditional lattice polytopes
Proves if-and-only-if equivalences for toric ring normality and quadratic toric ideal generation between anti-blocking lattice polytopes and their unconditional reflections, plus a graph-theoretic characterization of quadratic symmetric stable set ideals.
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Classification and counting of Gorenstein simplices with $h^*$-polynomial $1+t^k+\cdots+t^{(v-1)k}$
Gorenstein simplices with the given h*-polynomial are classified up to unimodular equivalence by strict divisor chains in the divisor lattice of v, yielding an explicit counting formula.