Closure relations for totally nonnegative cells in $G/P$. [PDF]
Mathematical Research Letters, 2006 12 pages, 1 figure, improved ...
Rietsch, K.
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Efficient Recognition of Totally Nonnegative Matrix Cells [PDF]
Foundations of Computational Mathematics, 2013 21p
Stéphane Launois, T. Lenagan
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Totally nonnegative cells and matrix Poisson varieties [PDF]
Advances in Mathematics, 2011 We describe explicitly the admissible families of minors for the totally nonnegative cells of real matrices, that is, the families of minors that produce nonempty cells in the cell decompositions of spaces of totally nonnegative matrices introduced by A. Postnikov.
Goodearl, K. R. +2 more
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Comprehensive analysis of metabolic pathway activity subtypes derived prognostic signature in hepatocellular carcinoma [PDF]
Cancer Medicine, 2023 Objective Metabolic reprogramming is one of the hallmarks of cancer, but metabolic pathway activity‐related subtypes of hepatocellular carcinoma (HCC) have not been identified.
Junyu Huo, Jinzhen Cai, Liqun Wu
doaj +2 more sources
Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves [PDF]
Mathematische Zeitschrift, 2010 The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the prime and primitive spectra of this algebra, the first step is to understand the prime ideals that are invariant under the torus action.
Goodearl, K. R. +2 more
openaire +5 more sources
Combinatorics of Positroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Recently Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroids.
Suho Oh
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Combinatorics of diagrams of permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 There are numerous combinatorial objects associated to a Grassmannian permutation $w_λ$ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook placements, acyclic orientations, various restricted fillings) and ...
Joel Brewster Lewis, Alejandro Morales
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Combinatorial formulas for ⅃-coordinates in a totally nonnegative Grassmannian, extended abstract, extended abstract [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Postnikov constructed a decomposition of a totally nonnegative Grassmannian $(Gr _{kn})_≥0$ into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point in $(Gr _{kn})_≥0$ belongs to and to determine affine ...
Kelli Talaska
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Pattern-Avoidance in Binary Fillings of Grid Shapes (short version) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 A $\textit{grid shape}$ is a set of boxes chosen from a square grid; any Young diagram is an example. This paper considers a notion of pattern-avoidance for $0-1$ fillings of grid shapes, which generalizes permutation pattern-avoidance.
Alexey Spiridonov
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Cuproptosis Combined with lncRNAs Predicts the Prognosis and Immune Microenvironment of Breast Cancer. [PDF]
Comput Math Methods Med, 2022 Zhang L +5 more
europepmc +1 more source