On sensitivity in bipartite Cayley graphs [PDF]
, 2020 Huang proved that every set of more than half the vertices of the $d$-dimensional hypercube $Q_d$ induces a subgraph of maximum degree at least $\sqrt{d}$, which is tight by a result of Chung, Füredi, Graham, and Seymour.
Garcia-Marco, Ignacio, Knauer, Kolja
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The Class of Non-Desarguesian Projective Planes is Borel Complete [PDF]
, 2018 For every infinite graph $\Gamma$ we construct a non-Desarguesian projective plane $P^*_{\Gamma}$ of the same size as $\Gamma$ such that $Aut(\Gamma) \cong Aut(P^*_{\Gamma})$ and $\Gamma_1 \cong \Gamma_2$ iff $P^*_{\Gamma_1} \cong P^*_{\Gamma_2 ...
Paolini, Gianluca
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Poisson spaces with a transition probability [PDF]
, 1996 The common structure of the space of pure states $P$ of a classical or a quantum mechanical system is that of a Poisson space with a transition probability.
Landsman, N. P.
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Sperner property and finite-dimensional Gorenstein algebras associated to matroids [PDF]
, 2016 We prove the Lefschetz property for a certain class of finite-dimensional Gorenstein algebras associated to matroids. Our result implies the Sperner property of the vector space lattice.
Maeno, Toshiaki, Numata, Yasuhide
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Beyond abstract elementary classes : On the model theory of geometric lattices [PDF]
, 2018 Based on Crapo’s theory of one point extensions of combinatorial geometries, we find various classes of geometric lattices that behave very well from the point of view of stability theory.
Hyttinen, Tapani, Paolini, Gianluca
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Highest weight modules and polarized embeddings of shadow spaces [PDF]
, 2010 Let Gamma be the K-shadow space of a spherical building Delta. An embedding V of Gamma is called polarized if it affords all "singular" hyperplanes of Gamma. Suppose that Delta is associated to a Chevalley group G. Then Gamma can be embedded into what we
Rieuwert J. Blok, Rieuwert J. Blok
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Desargues maps and the Hirota-Miwa equation [PDF]
, 2009 We study the Desargues maps $\phi:\ZZ^N\to\PP^M$, which generate lattices whose points are collinear with all their nearest (in positive directions) neighbours.
Akhmetshin A. A. +26 more
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Decomposition and Structure theorems for Garside-like groups with modular lattice structure
, 2023 Despite being a vast generalization of Garside groups, right $\ell$-groups with noetherian lattice structure and strong order unit share a lot of the properties of Garside groups.
Dietzel, Carsten
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Algebarsko modeliranje kvantno-mehaničkih jednadžbi u konačno i beskonačno dimenzionalnim Hilbertovim prostorima [PDF]
, 2011 The Hilbert space of quantum mechanics has a dual representation in lattice theory, called the Hilbert lattice. In addition to offering the potential for new insights, the lattice-theoretical approach may be computationally efficient for certain kinds of
Megill, Norman Dwight
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Foundations of matroids -- Part 2: Further theory, examples, and computational methods
, 2023 In this sequel to "Foundations of matroids - Part 1", we establish several presentations of the foundation of a matroid in terms of small building blocks.
Baker, Matthew +2 more
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