CO-UNIVERSAL C*-ALGEBRAS ASSOCIATED TO APERIODIC k-GRAPHS [PDF]
Glasgow Mathematical Journal, 2013 AbstractWe construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space $\mathcal{H}^{\rm ap}$ with basis indexed by aperiodic boundary paths in Λ. We show that the canonical expectation on $\mathcal{B}(\mathcal{H}^{\rm ap})$ restricts to an expectation of the image of this representation onto the subalgebra spanned by ...
Kang, Sooran, Sims, Aidan
core +8 more sources
Aperiodicity and cofinality for finitely aligned higher-rank graphs [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2010 AbstractWe introduce new formulations of aperiodicity and cofinality for finitely aligned higher-rank graphs Λ, and prove thatC*(Λ) is simple if and only if Λ is aperiodic and cofinal. The main advantage of our versions of aperiodicity and cofinality over existing ones is that ours are stated in terms of finite paths. To prove our main result, we first
Lewin, Peter, Sims, Aidan
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Graph Theoretic Analyses of Tessellations of Five Aperiodic Polykite Unitiles [PDF]
MathematicsAperiodic tessellations of polykite unitiles, such as hats and turtles, and the recently introduced hares, red squirrels, and gray squirrels, have attracted significant interest due to their structural and combinatorial properties.
John R. Jungck, Purba Biswas
doaj +3 more sources
Average scattering entropy for periodic, aperiodic and random distribution of vertices in simple quantum graphs [PDF]
Physica E: Low-dimensional Systems and Nanostructures, 2022 8 pages, 16 figures, accepted for publication in Physica ...
Alison A. Silva +2 more
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Aperiodicity conditions in topological $k$-graphs [PDF]
Journal of Operator Theory, 2014 12 pages, 3 figures, in version 2 the statement of the third condition has been ...
Sarah E. Wright
+7 more sources
Spectra of Schreier graphs of Grigorchuk’s group and Schroedinger operators with aperiodic order [PDF]
Mathematische Annalen, 2017 Article to appear in Math. Ann.; part of the study of combinatorics of the subshift removed and included in arXiv:1711.10342; apart from this only minor ...
Rostislav Grigorchuk +2 more
+7 more sources
Limit aperiodic and repetitive colorings of graphs [PDF]
, 2018 Let $X$ be a (repetitive) infinite connected simple graph with a finite upper bound $ $ on the vertex degrees. The main theorem states that $X$ admits a (repetitive) limit aperiodic vertex coloring by $ $ colors. This refines a theorem for finite graphs proved by Collins and Trenk, and by Klav ar, Wong and Zhu, independently. It is also related to a
López, Jesús A. Álvarez +1 more
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A bijection between aperiodic palindromes and connected circulant graphs [PDF]
, 2014 In this paper, we show that there is a one-to-one correspondence between the set of compositions (resp. prime compositions) of $n$ and the set of circulant digraphs (resp. connected circulant digraphs) of order $n$. We also show that there is a one-to-one correspondence between the set of palindromes (resp.
Baek, Hunki +3 more
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Random colourings of aperiodic graphs: Ergodic and spectral properties [PDF]
, 2007 26 ...
Müller, Peter, Richard, Christoph
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Aperiodicity and the primitive ideal space of a row-finite $k$-graph $C^*$-algebra [PDF]
, 2011 We describe the primitive ideal space of the $C^{\ast}$-algebra of a row-finite $k$-graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces can occur, and compute the primitive ideal space of two examples. In order to do this we prove some new results on aperiodicity.
Kang, Sooran, Pask, David
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