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The Spectre is an aperiodic monotile for the Euclidean plane that is truly chiral in the sense that it tiles the plane without any need for a reflected tile. The topological and dynamical properties of the Spectre tilings are very similar to those of
Externí odkaz:
http://arxiv.org/abs/2411.15503
Autor:
Baake, Michael, Mañibo, Neil
Publikováno v:
Coll. Math. 176 (2024), 121--134
The sets of $\cB$-free integers are considered with respect to (reversing) symmetries. It is well known that, for a large class of them, the centraliser of the associated $\cB$-free shift (otherwise known as its automorphism group) is trivial. We ext
Externí odkaz:
http://arxiv.org/abs/2406.15242
Autor:
Baake, Ellen, Baake, Michael
The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the context of m
Externí odkaz:
http://arxiv.org/abs/2406.09430
Autor:
Baake, Ellen, Baake, Michael
The embedding problem of Markov transition matrices into Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the well-known coupon collection pr
Externí odkaz:
http://arxiv.org/abs/2405.05203
Autor:
Baake, Michael, Sumner, Jeremy
Markov matrices of equal-input type constitute a widely used model class. The corresponding equal-input generators span an interesting subalgebra of the real matrices with zero row sums. Here, we summarise some of their amazing properties and discuss
Externí odkaz:
http://arxiv.org/abs/2404.11222
Publikováno v:
Lett. Math. Phys. 114 (2024) 101:1-12
The aim of this note is to show the existence of a large family of Cantorvals arising in the projection description of primitive two-letter substitutions. This provides a common and naturally occurring class of Cantorvals.
Comment: 11 pages, 3 f
Comment: 11 pages, 3 f
Externí odkaz:
http://arxiv.org/abs/2401.05372
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the well-known
Externí odkaz:
http://arxiv.org/abs/2311.05387
Orbit separation dimension (OSD), previously introduced as amorphic complexity, is a powerful complexity measure for topological dynamical systems with pure-point spectrum. Here, we develop methods and tools for it that allow a systematic application
Externí odkaz:
http://arxiv.org/abs/2311.03541
Autor:
Baake, Michael, Sumner, Jeremy
Publikováno v:
J. Math. Biol. 89 (2024) 23:1--45
The embedding problem of Markov matrices in Markov semigroups is a classic problem that regained a lot of impetus and activities through recent needs in phylogeny and population genetics. Here, we give an account for dimensions $d\leqslant 4$, includ
Externí odkaz:
http://arxiv.org/abs/2311.02596
Autor:
Baake, Michael, Haynes, Alan
It is well known that the Fourier--Bohr coefficients of regular model sets exist and are uniformly converging, volume-averaged exponential sums. Several proofs for this statement are known, all of which use fairly abstract machinery. For instance, th
Externí odkaz:
http://arxiv.org/abs/2308.07105