Counterexample to Ziegler's conjecture: explicit simplicial 7-dimensional 0/1-polytope with 14 vertices that is not centrally symmetric, plus enumeration of all such examples in dimension 7.
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Springer-Verlag, New York, 1995, pp
12 Pith papers cite this work. Polarity classification is still indexing.
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Closed-form solutions are provided for a family of nonconvex optimization problems on ratios of principal minor products for positive definite matrices, confirming the Ingleton ratio infimum is 16/27 for 4x4 matrices.
A one-to-one correspondence maps maximal LDP channels under the Blackwell order to vertices of a finite-dimensional polytope, making optimal privacy-utility trade-offs computable via linear programming or vertex enumeration for general problems.
Introduces priced face-crossing via normal-fan geometry on occupancy polytopes to decompose dynamic regret into intrinsic motion cost plus within-face error in non-stationary adversarial MDPs.
Constructs flag simplicial spheres with independence number asymptotically equal to vertex count, disproving Chudnovsky-Nevo conjecture.
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.
A complete linear inequality description and volume formula are derived for the convex hull of the graph of a monomial on a nonnegative box with at most one positive lower bound.
An analog of Cauchy's surface area formula is established for Funk geometry on a convex body K using Holmes-Thompson area and central projections, reducing to a weighted vertex sum for polytopes and yielding a generalized Crofton formula.
c-Birkhoff polytopes are unimodularly equivalent to the order polytopes of the heap posets of the c-sorting words of the longest permutation.
Adjacency Sampling reproduces all known Bell inequality classes in solved cases and generates over 129 million classes for the L_{3,3,3,3} scenario plus millions more for larger ones.
Formalizes PCTL on MJLSs to specify and check moment-based stability properties for prescribed initial state sets using linear-algebraic techniques.
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Stability Checking of Markov Jump Linear Systems via Probabilistic Temporal Logic (Extended Version)
Formalizes PCTL on MJLSs to specify and check moment-based stability properties for prescribed initial state sets using linear-algebraic techniques.