102 research outputs found

    Non-Injectivity of Infinite Interval Exchange Transformations and Generalized Thue-Morse Sequences

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    In this paper we study the non-injectivity arising in infinite interval exchange transformations. In particular, we build and analyze an infinite family of infinite interval exchanges semi-conjugated to generalized Thue-Morse subshifts, whose non-injectivity occurs at a characterizable finite set of points.Comment: 23 pages, 8 figure

    Arithmetical subword complexity of automatic sequences

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    We fully classify automatic sequences aa over a finite alphabet Ω\Omega with the property that each word over Ω\Omega appears is aa along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal possible arithmetical subword complexity. More generally, we obtain an asymptotic formula for arithmetical (and even polynomial) subword complexity of a given automatic sequence aa.Comment: 14 pages, comments welcom

    Review of Particle Physics

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    The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.United States Department of Energy (DOE) DE-AC02-05CH11231government of Japan (Ministry of Education, Culture, Sports, Science and Technology)Istituto Nazionale di Fisica Nucleare (INFN)Physical Society of Japan (JPS)European Laboratory for Particle Physics (CERN)United States Department of Energy (DOE

    On a generalization of Abelian equivalence and complexity of infinite words

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    In this paper we introduce and study a family of complexity functions of infinite words indexed by k in Z^+ U {+infinity}. Let k in Z^+ U {+infinity} and A be a finite non-empty set. Two finite words u and v in A* are said to be k-Abelian equivalent if for all x in A* of length less than or equal to k, the number of occurrences of x in u is equal to the number of occurrences of x in v. This defines a family of equivalence relations sim_k on A*, bridging the gap between the usual notion of Abelian equivalence (when k = 1) and equality (when k = +infinity). We show that the number of k-Abelian equivalence classes of words of length n grows polynomially, although the degree is exponential in k. Given an infinite word omega in A^N, we consider the associated complexity function P^(k)_omega : N -> N which counts the number of k-Abelian equivalence classes of factors of omega of length n. We show that the complexity function P_k is intimately linked with periodicity. More precisely we define an auxiliary function q^k : N -> N and show that if P^(k)_omega(n) < q^k(n) for some k in Z^+ U {+infinity} and n >= 0, then omega is ultimately periodic. Moreover if omega is aperiodic, then P^(k)_omega(n) = q^k(n) if and only if omega is Sturmian. We also study k-Abelian complexity in connection with repetitions in words. Using Szemeredi's theorem, we show that if omega has bounded k-Abelian complexity, then for every D subset of N with positive upper density and for every positive integer N, there exists a k-Abelian N-power occurring in omega at some position j in D

    On the {S}kolem Problem and the {S}kolem Conjecture

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    A Note On â„“\ell-Rauzy Graphs for the Infinite Fibonacci Word

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    The ℓ\ell-Rauzy graph of order kk for any infinite word is a directed graph in which an arc (v1,v2)(v_1,v_2) is formed if the concatenation of the word v1v_1 and the suffix of v2v_2 of length k−ℓk-\ell is a subword of the infinite word. In this paper, we consider one of the important aperiodic recurrent words, the infinite Fibonacci word for discussion. We prove a few basic properties of the ℓ\ell-Rauzy graph of the infinite Fibonacci word. We also prove that the ℓ\ell-Rauzy graphs for the infinite Fibonacci word are strongly connected.Comment: 10 pages, 4 figure

    Review of Particle Physics

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    The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app
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