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Graph Theory versus Minimum Rank for Index Coding [PDF]
2014 IEEE International Symposium on Information Theory, 2014 We obtain novel index coding schemes and show that they provably outperform all previously known graph theoretic bounds proposed so far. Further, we establish a rather strong negative result: all known graph theoretic bounds are within a logarithmic ...
Karthikeyan Shanmugam +2 more
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A dual graph construction for higher-rank graphs, and 𝐾-theory for finite 2-graphs [PDF]
Proceedings of the American Mathematical Society, 2005 Given a $k$-graph $\Lambda$ and an element $p$ of $\NN^k$, we define the dual $k$-graph, $p\Lambda$. We show that when $\Lambda$ is row-finite and has no sources, the $C^*$-algebras $C^*(\Lambda)$ and $C^*(p\Lambda)$ coincide.
Stephen Allen, David Pask, Aidan Sims
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Real and complex K-theory for higher rank graph algebras arising from cube complexes [PDF]
Annals of K-TheoryUsing the Evans spectral sequence and its counter-part for real $K$-theory, we compute both the real and complex $K$-theory of several infinite families of $C^*$-algebras based on higher-rank graphs of rank $3$ and $4$. The higher-rank graphs we consider
Jeffrey L. Boersema, Alina Vdovina
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On the
Journal of Mathematical Analysis and Applications, 2012 We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott's computation of the K-theory of the rotation algebras.
Alex Kumjian, David Pask, Aidan Sims
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THE K-THEORY OF THE -ALGEBRAS OF 2-RANK GRAPHS ASSOCIATED TO COMPLETE BIPARTITE GRAPHS [PDF]
Journal of the Australian Mathematical Society, 2021 AbstractUsing a result of Vdovina, we may associate to each complete connected bipartite graph$\kappa $a two-dimensional square complex, which we call a tile complex, whose link at each vertex is$\kappa $. We regard the tile complex in two different ways, each having a different structure as a$2$-rank graph.
Sam A. Mutter
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Structure theory and stable rank for C*-algebras of finite higher-rank graphs [PDF]
Proceedings of the Edinburgh Mathematical Society, 2021 AbstractWe study the structure and compute the stable rank of$C^{*}$-algebras of finite higher-rank graphs. We completely determine the stable rank of the$C^{*}$-algebra when the$k$-graph either contains no cycle with an entrance or is cofinal. We also determine exactly which finite, locally convex$k$-graphs yield unital stably finite$C^{*}$-algebras ...
David Pask, Adam Sierakowski, Aidan Sims
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$C^{\star}$-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory [PDF]
Publicacions Matemàtiques, 2023 We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action on the product of trees defines a $k$-dimensional cube complex, which induces a higher-rank graph.
Sam A. Mutter +2 more
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K-theory and homotopies of 2-cocycles on higher-rank graphs [PDF]
Pacific Journal of Mathematics, 2015 This paper continues our investigation into the question of when a homotopy $ = \{ _t\}_{t \in [0,1]}$ of 2-cocycles on a locally compact Hausdorff groupoid $\mathcal{G}$ gives rise to an isomorphism of the $K$-theory groups of the twisted groupoid $C^*$-algebras: $K_*(C^*(\mathcal{G}, _0)) \cong K_*(C^*(\mathcal{G}, _1)).$ In particular, we ...
Elizabeth Gillaspy
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Remote Sensing, 2020 The accuracy of anomaly detection in hyperspectral images (HSIs) faces great challenges due to the high dimensionality, redundancy of data, and correlation of spectral bands.
Shangzhen Song +3 more
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A Note on Brill–Noether Theory and Rank-Determining Sets for Metric Graphs [PDF]
International Mathematics Research Notices, 2012 We produce open subsets of the moduli space of metric graphs without separating edges where the dimensions of Brill-Noether loci are larger than the corresponding Brill-Noether numbers. These graphs also have minimal rank determining sets that are larger than expected, giving couterexamples to a conjecture of Luo.
Chang Mou Lim +2 more
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