Purity And Separation For Oriented Matroids
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Purity And Separation For Oriented Matroids
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Author : Pavel Galashin
language : en
Publisher:
Release Date : 2023
Purity And Separation For Oriented Matroids written by Pavel Galashin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Combinatorial analysis categories.
Leclerc and Zelevinsky, motivated by the study of quasi-commuting quantum flag minors, introduced the notions of strongly separated and weakly separated collections. These notions are closely related to the theory of cluster algebras, to the combinatorics of the double Bruhat cells, and to the totally positive Grassmannian. A key feature, called the purity phenomenon, is that every maximal by inclusion strongly (resp., weakly) separated collection of subsets in [n] has the same cardinality. In this paper, we extend these notions and define M-separated collections for any oriented matroid M. We show that maximal by size M-separated collections are in bijection with fine zonotopal tilings (if M is a realizable oriented matroid), or with one-element liftings of M in general position (for an arbitrary oriented matroid). We introduce the class of pure oriented matroids for which the purity phenomenon holds: an oriented matroid M is pure if M-separated collections form a pure simplicial complex, i.e., any maximal by inclusion M-separated collection is also maximal by size. We pay closer attention to several special classes of oriented matroids: oriented matroids of rank 3, graphical oriented matroids, and uniform oriented matroids. We classify pure oriented matroids in these cases. An oriented matroid of rank 3 is pure if and only if it is a positroid (up to reorienting and relabeling its ground set). A graphical oriented matroid is pure if and only if its underlying graph is an outerplanar graph, that is, a subgraph of a triangulation of an n-gon. We give a simple conjectural characterization of pure oriented matroids by forbidden minors and prove it for the above classes of matroids (rank 3, graphical, uniform).
Purity And Separation For Oriented Matroids
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Author : Pavel Galashin
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-27
Purity And Separation For Oriented Matroids written by Pavel Galashin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-27 with Mathematics categories.
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Syz Geometry For Calabi Yau 3 Folds Taub Nut And Ooguri Vafa Type Metrics
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Author : Yang Li
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-26
Syz Geometry For Calabi Yau 3 Folds Taub Nut And Ooguri Vafa Type Metrics written by Yang Li and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-26 with Mathematics categories.
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Finite Groups Which Are Almost Groups Of Lie Type In Characteristic Mathbf P
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Author : Chris Parker
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-26
Finite Groups Which Are Almost Groups Of Lie Type In Characteristic Mathbf P written by Chris Parker and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-26 with Mathematics categories.
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The Space Of Spaces Curvature Bounds And Gradient Flows On The Space Of Metric Measure Spaces
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Author : Karl-Theodor Sturm
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-27
The Space Of Spaces Curvature Bounds And Gradient Flows On The Space Of Metric Measure Spaces written by Karl-Theodor Sturm and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
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Eulerian Spaces
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Author : Paul Gartside
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-26
Eulerian Spaces written by Paul Gartside and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-26 with Mathematics categories.
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P Dg Cyclotomic Nilhecke Algebras Ii
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Author : You Qi
language : en
Publisher: American Mathematical Society
Release Date : 2024-02-01
P Dg Cyclotomic Nilhecke Algebras Ii written by You Qi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-01 with Mathematics categories.
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The Generation Problem In Thompson Group F
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Author : Gili Golan Polak
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-26
The Generation Problem In Thompson Group F written by Gili Golan Polak and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-26 with Mathematics categories.
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Sur Un Probl Me De Compatibilit Local Global Localement Analytique
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Author : Christophe Breuil
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-27
Sur Un Probl Me De Compatibilit Local Global Localement Analytique written by Christophe Breuil and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
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Potential Estimates And Quasilinear Parabolic Equations With Measure Data
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Author : Quoc-Hung Nguyen
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-19
Potential Estimates And Quasilinear Parabolic Equations With Measure Data written by Quoc-Hung Nguyen and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-19 with Mathematics categories.
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