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Project B2: Combinatorial and topological structure of aperiodic tilings



Summary:

In this project, we investigate the combinatorial and topological structure of tiling spaces, as well as related lattice problems. Tiling spaces are typically obtained as the hull of one or several tilings under the action of the translation group. In particular, we study the close relations between the combinatorial and geometric properties of the individual tilings, the topological properties of the tiling space, and the properties of the dynamical system under the translation action.



Recent Preprints:

17027 Michael Baake, Natalie Frank, Uwe Grimm, E. Arthur Robinson, Jr. PDF

Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction

Project: B2

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Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction


Authors: Michael Baake, Natalie Frank, Uwe Grimm, E. Arthur Robinson, Jr. Projects: B2
Submission Date: 2017-06-30 Submitter: Franz Gähler
Download: PDF Link: 17027

17024 Chrizaldy Neil C. Manibo PDF

Lyapunov exponents for binary substitutions of constant length

Project: A1, B2

Published: J. Math. Phys. 58 (2017), 9pp

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Lyapunov exponents for binary substitutions of constant length


Authors: Chrizaldy Neil C. Manibo Projects: A1, B2
Submission Date: 2017-06-30 Submitter: Michael Baake
Download: PDF Link: 17024
Published: J. Math. Phys. 58 (2017), 9pp

16060 Michael Baake, David Damanik, Uwe Grimm PDF

What is Aperiodic Order?

Project: A1, B2

Published: Notices AMS 63 (2016), 647-650

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What is Aperiodic Order?


Authors: Michael Baake, David Damanik, Uwe Grimm Projects: A1, B2
Submission Date: 2018-01-23 Submitter: Franz Gähler
Download: PDF Link: 16060
Published: Notices AMS 63 (2016), 647-650

16056 Michael Baake, David Écija, Uwe Grimm PDF

A guide to lifting aperiodic structures

Project: B2

Published: Z. Krist. 231 (2016), 507-515

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A guide to lifting aperiodic structures


Authors: Michael Baake, David Écija, Uwe Grimm Projects: B2
Submission Date: 2017-04-12 Submitter: Christian Huck
Download: PDF Link: 16056
Published: Z. Krist. 231 (2016), 507-515

15075 Shigeki Akiyama, Franz Gähler, Jeong-Yup Lee PDF

Determining pure discrete spectrum for some self-affine tilings

Project: B2

Published: Disc. Math. Th. Comp. Sci. (DMTCS), no. 16:3 (2014), 305-316

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Determining pure discrete spectrum for some self-affine tilings


Authors: Shigeki Akiyama, Franz Gähler, Jeong-Yup Lee Projects: B2
Submission Date: 2015-12-15 Submitter: Michael Baake
Download: PDF Link: 15075
Published: Disc. Math. Th. Comp. Sci. (DMTCS), no. 16:3 (2014), 305-316

15061 Michael Baake, Franz Gähler PDF

Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples

Project: B2

Published: Topol. Appl. 205 (2016) 205 (2016), 4-27

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Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples


Authors: Michael Baake, Franz Gähler Projects: B2
Submission Date: 2015-12-14 Submitter: Christian Huck
Download: PDF Link: 15061
Published: Topol. Appl. 205 (2016) 205 (2016), 4-27

15053 Leo Margolis PDF

Subgroup Isomorphism Problem for Units of Integral Group Rings

Project: B2

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Subgroup Isomorphism Problem for Units of Integral Group Rings


Authors: Leo Margolis Projects: B2
Submission Date: 2015-11-26 Submitter: Michael Baake
Download: PDF Link: 15053

14031 Franz Gähler, Eden Miro PDF

Topology of the Random Fibonacci Tiling Space

Project: B2

Published: Acta Phys. Pol., no. 126 (2014), 564-567

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Topology of the Random Fibonacci Tiling Space


Authors: Franz Gähler, Eden Miro Projects: B2
Submission Date: 2014-05-20 Submitter: Michael Baake
Download: PDF Link: 14031
Published: Acta Phys. Pol., no. 126 (2014), 564-567

14030 Enrico Paolo Bugarin, Franz Gähler PDF

Quotient cohomology of certain 1- and 2-dimensional substitution tiling spaces

Project: B2

Published: Acta Phys. Pol., no. 126 (2014), 438-441

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Quotient cohomology of certain 1- and 2-dimensional substitution tiling spaces


Authors: Enrico Paolo Bugarin, Franz Gähler Projects: B2
Submission Date: 2014-05-20 Submitter: Michael Baake
Download: PDF Link: 14030
Published: Acta Phys. Pol., no. 126 (2014), 438-441

14029 Franz Gähler, Eugene E. Kwan, Gregory R. Maloney PDF

A computer search for planar substitution tilings with n-fold rotational symmetry

Project: B2

Published: Discrete Comput. Geom., no. 53 (2015), 445-465

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A computer search for planar substitution tilings with n-fold rotational symmetry


Authors: Franz Gähler, Eugene E. Kwan, Gregory R. Maloney Projects: B2
Submission Date: 2014-05-20 Submitter: Michael Baake
Download: PDF Link: 14029
Published: Discrete Comput. Geom., no. 53 (2015), 445-465



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