{"total":12,"items":[{"citing_arxiv_id":"2606.31640","ref_index":15,"ref_count":2,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A Counterexample to Ziegler's Cross-Polytope Conjecture for Simplicial 0/1-Polytopes","primary_cat":"math.CO","submitted_at":"2026-06-30T13:21:48+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.29092","ref_index":42,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Priced Motion Through Optimal Faces: A Normal-Fan Geometry for Non-Stationary Adversarial MDPs","primary_cat":"cs.LG","submitted_at":"2026-06-27T21:20:26+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.24880","ref_index":24,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Stability Checking of Markov Jump Linear Systems via Probabilistic Temporal Logic (Extended Version)","primary_cat":"cs.LO","submitted_at":"2026-06-23T17:55:48+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Formalizes PCTL on MJLSs to specify and check moment-based stability properties for prescribed initial state sets using linear-algebraic techniques.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.23632","ref_index":43,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Sharp Inequalities for Products of Principal Minors of Positive Definite Matrices","primary_cat":"math.MG","submitted_at":"2026-06-22T17:23:30+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.16109","ref_index":5,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Large Independent Sets in Flag Spheres","primary_cat":"math.CO","submitted_at":"2026-06-15T01:54:25+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Constructs flag simplicial spheres with independence number asymptotically equal to vertex count, disproving Chudnovsky-Nevo conjecture.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.15970","ref_index":136,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Copositive Matrices with Ordered Off-Diagonal Entries","primary_cat":"math.OC","submitted_at":"2026-05-15T14:00:47+00:00","verdict":"UNVERDICTED","verdict_confidence":"UNKNOWN","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.02479","ref_index":23,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Frobenius identities for the volume map on Cohen--Macaulay rings","primary_cat":"math.AC","submitted_at":"2026-05-04T11:24:34+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"schetz property? We address this question in characteristic two, see Section 5, and use the Parseval-Rayleigh iden- tity to prove the anisotropy for the generic Pfaffian in characteristic two (which, in turn, implies that for characteristic zero). This gives a new proof for the generic Lefschetz property, which was previously shown using different methods [AAI+23]. We also provide some additional examples of Parseval-Rayleigh identities on Gorenstein rings in Section 7, hinting at future developments. There are many open conjectures about the Lefschetz properties of generic Artinian reductions on Cohen-Macaulay and Gorenstein rings. For example, Migliore and Nagel ask if the generic Artinian reductions of reduced standardk-algebras have the weak Lefschetz property [MN13,"},{"citing_arxiv_id":"2605.02319","ref_index":38,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Optimal Privacy-Utility Trade-Offs in LDP: Functional and Geometric Perspectives","primary_cat":"cs.CR","submitted_at":"2026-05-04T08:15:48+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Athena Scientific, 1st edition, January 1997. ISBN 978-1-886529-19-9. [36] Günter M. Ziegler.Lectures on Polytopes, volume 152 ofGraduate Texts in Mathematics. Springer, New York, NY , 1995. ISBN 978-0-387-94365-7 978-1-4613-8431-1. doi: 10.1007/978-1-4613-8431-1. [37] R. Tyrrell Rockafellar.Convex Analysis. Princeton University Press, January 1997. ISBN 978-0-691- 01586-6. [38] Erich L. Lehmann and George Casella.Theory of Point Estimation. Springer Texts in Statistics. Springer- Verlag, New York, 1998. ISBN 978-0-387-98502-2. doi: 10.1007/b98854. 12 A Convex Geometry We characterize maximal LDP channels using convex-geometric approaches. For a comprehensive treatment of the concepts in this subsection, we refer the reader to standard texts [35-37]."},{"citing_arxiv_id":"2605.01493","ref_index":3,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"On the convex hull of the graph of a simple monomial","primary_cat":"math.OC","submitted_at":"2026-05-02T15:29:58+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.22859","ref_index":26,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Bell Inequalities from Polyhedral Sampling","primary_cat":"quant-ph","submitted_at":"2026-04-22T20:09:20+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2601.16468","ref_index":36,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Cauchy's Surface Area Formula in the Funk Geometry","primary_cat":"cs.CG","submitted_at":"2026-01-23T05:58:12+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2504.07505","ref_index":14,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"$c$-Birkhoff polytopes","primary_cat":"math.CO","submitted_at":"2025-04-10T07:05:41+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"c-Birkhoff polytopes are unimodularly equivalent to the order polytopes of the heap posets of the c-sorting words of the longest permutation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}