The cross-product conjecture for width two posets

DOI10.1090/tran/8679zbMath1496.05010arXiv2104.09009OpenAlexW4214879484MaRDI QIDQ5100036

Igor Pak, Swee Hong Chan, Greta Panova

Publication date: 29 August 2022

Full work available at URL: https://arxiv.org/abs/2104.09009

zbMATH Keywords

lattice path\(q\)-analoguelog-concavity\(1/3\)-\(2/3\) conjecturelinear extensions of posetsLindström-Gessel-Viennot lemmaStanley inequalitycross-product conjectureGraham-Yao-Yao inequalityKahn-Saks inequalityXYZ inequality

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Combinatorics of partially ordered sets (06A07) Combinatorial inequalities (05A20) Algebraic aspects of posets (06A11)

Related Items

Extensions of the Kahn-Saks inequality for posets of width two, Effective Poset Inequalities, Enumerative combinatorics. Abstracts from the workshop held December 11--17, 2022, Log-concave poset inequalities (extended abstract), Multivariate correlation inequalities for \(P\)-partitions

Cites Work

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• On \(q\)-integrals over order polytopes
• A combinatorial approach to height sequences in finite partially ordered sets
• Two combinatorial applications of the Aleksandrov-Fenchel inequalities
• The XYZ conjecture and the FKG inequality
• Counting linear extensions
• How good is the information theory bound in sorting?
• A family of partially ordered sets with small balance constant
• Balancing pairs and the cross product conjecture
• Improving the \(\frac{1}{3}\)-\(\frac{2}{3}\) conjecture for width two posets
• Spectral lower bounds for the quantum chromatic number of a graph. II
• Lorentzian polynomials
• Balancing poset extensions
• A correlational inequality for linear extensions of a poset
• Negative dependence and the geometry of polynomials
• The Information-Theoretic Bound is Good for Merging
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
• Some Monotonicity Properties of Partial Orders
• The FKG Inequality and Some Monotonicity Properties of Partial Orders
• Correlation Among Partial Orders
• Sorting probability for large Young diagrams
• COMBINATORIAL APPLICATIONS OF THE HODGE–RIEMANN RELATIONS
• Combinatorial Inequalities