Results 91 to 100 of about 1,406 (208)
On Stanley's chromatic symmetric function and clawfree graphs
Discrete Mathematics, 1999 A proper coloring of a simple graph \(G\) (without loops and multiple edges) with vertex set \(V=\{v_1,\ldots,v_d\}\) is a function \(\kappa: V\to {\mathbb{N}}^+\) such that \(\kappa(u)\not=\kappa(v)\) if \(u\) and \(v\) are vertices of an edge of \(G\).
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Splitting the cohomology of Hessenberg varieties and e-positivity of chromatic symmetric functions
, 2023 For each indifference graph, there is an associated regular semisimple Hessenberg variety, whose cohomology recovers the chromatic symmetric function of the graph.
Abreu, Alex, Nigro, Antonio
core
Evaluating anisotropy‐based Monin–Obukhov similarity theory over canopies and complex terrain
Quarterly Journal of the Royal Meteorological Society, EarlyView.This study shows that an anisotropy‐based generalization of Monin–Obukhov surface‐layer scaling (SC23) applies readily across a wide range of atmospheric conditions with variable terrain, canopies, and land‐cover complexity. This work focuses on the scaling of velocity variances for 7 years at the 47 sites in the National Ecological Observation Network
Tyler S. Waterman +3 more
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Responsive Materials, EarlyView.Machine learning provides a unifying framework to connect structure, fluorescence properties, and applications of carbon‐based quantum dots. This review highlights how data‐driven strategies enable fluorescence regulation, reveal underlying mechanisms, and accelerate the rational design of functional carbon dots.
Liangfeng Chen +8 more
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Small, EarlyView.This work reports a differentiated ion‐doping strategy to engineer the self‐trapped exciton emission of CsPbBr3@CsPb2Br5 nanostructures, in which bright orange emission is obtained by the dissolution and recrystallization of Cu:CsPbBr3 in water. Lattice‐incorporated Cu components create self‐trapped exciton centers because of bright green emission ...
Wenbin Shi +4 more
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Small Methods, EarlyView.Quantitative dual‐color STORM imaging provides direct nanoscale measurement of protein coronas on nanoparticles in biological media. The approach reveals consistent ∼50 nm corona layers, establishing a reproducible method for characterizing the nanomaterial‐protein interfaces.
Bradley T. Cech +2 more
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The Chromatic Symmetric Function of Graphs Glued at a Single Vertex
The Electronic Journal of CombinatoricsWe describe how the chromatic symmetric function of two graphs glued at a single vertex can be expressed as a matrix multiplication using certain information of the two individual graphs. We then prove new $e$-positivity results by using a connection between forest triples, defined by the first author, and Hikita's probabilities associated to standard ...
Foster Tom, Aarush Vailaya
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Down-up algebras and chromatic symmetric functions
International audienceWe establish Guay-Paquet's unpublished linear relation between certain chromatic symmetric functions by relating his algebra on paths to the $q$-Klyachko algebra.
Nadeau, Philippe, Tewari, Vasu
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Chromatic Symmetric Functions and H-free Graphs
, 2017 A key area of investigation in chromatic symmetric functions concerns the e-positivity, and/or Schur positivity, of a particular class of chromatic symmetric functions whose underlying graphs are clawfree.
Hamel, Angele
core
Chromatic functions, interval orders and increasing forests [PDF]
The chromatic quasisymmetric functions (csf) of Shareshian and Wachs associated to unit interval orders have attracted a lot of interest since their introduction in 2016, both in combinatorics and geometry, because of their relation to the famous Stanley-
Siconolfi, Viola +2 more
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