Abstract:
In this paper we consider one-dimensional quasiperiodic tilings based on the use of irrational rotations of a circle.
We completely describe a wide class of progressions included in the mentioned tilings.
This publication is cited in the following 14 articles:
A. A. Zhukova, A. V. Shutov, “Additivnaya zadacha s $k$ chislami spetsialnogo vida”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii “Aktualnye problemy prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 22–26 maya 2018 g. Chast II, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 166, VINITI RAN, M., 2019, 10–21
Shutov A. Maleev A., “Coordination Shells and Coordination Numbers of the Vertex Graph of the Ammann-Beenker Tiling”, Acta Crystallogr. Sect. A, 75:5 (2019), 746–757
A. A. Zhukova, A. V. Shutov, “Geometrizatsiya sistem schisleniya”, Chebyshevskii sb., 18:4 (2017), 222–245
A. V. Shutov, “Trigonometric Integrals over One-Dimensional Quasilattices of Arbitrary Codimension”, Math. Notes, 99:4 (2016), 590–597
E. P. Davletyarova, A. A. Zhukova, A. V. Shutov, “Geometrizatsiya obobschennykh sistem schisleniya Fibonachchi i ee prilozheniya k teorii chisel”, Chebyshevskii sb., 17:2 (2016), 88–112
A. V. Shutov, “Trigonometric Sums over One-Dimensional Quasilattices of Arbitrary Codimension”, Math. Notes, 97:5 (2015), 791–802
A. A. Zhukova, A. V. Shutov, “Binarnaya additivnaya zadacha s chislami spetsialnogo vida”, Chebyshevskii sb., 16:3 (2015), 246–275
Kelly M., Sadun L., “Pattern Equivariant Cohomology and Theorems of Kesten and Oren”, Bull. London Math. Soc., 47:1 (2015), 13–20
V. G. Zhuravlev, “Imbedding of circular orbits and the distribution of fractional parts”, St. Petersburg Math. J., 26:6 (2015), 881–909
A. V. Shutov, “Mnogomernye obobscheniya summ drobnykh dolei i ikh teoretiko-chislovye prilozheniya”, Chebyshevskii sb., 14:1 (2013), 104–118
E. P. Davletyarova, A. A. Zhukova, A. V. Shutov, “Geometrization of Fibonacci numeration system and its applications to number theory”, St. Petersburg Math. J., 25:6 (2014), 893–907
V. V. Krasil'shchikov, A. V. Shutov, “Distribution of points of one-dimensional quasilattices with respect to a variable module”, Russian Math. (Iz. VUZ), 56:3 (2012), 14–19
A. V. Shutov, “Trigonometricheskie summy nad odnomernymi kvazireshetkami”, Chebyshevskii sb., 13:2 (2012), 136–148
V. V. Krasil'shchikov, A. V. Shutov, “Description and Exact Maximum and Minimum Values of the Remainder in the Problem of the Distribution of Fractional Parts”, Math. Notes, 89:1 (2011), 59–67
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