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Periodic sets of integers
1994
Theoretical Computer Science
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., Periodic sets of integers, Theoretical Computer Science 127 (1994) 287-312. ...
Consider the following kinds of sets: _ the set of all possible distances between two vertices of a directed graph; _ any set of integers that is either finite or periodic for all n greater or equal to ...
Type 2
Ultimately periodic sets of integers
Type 3
Ultimately periodic sets of integers
Theorem 3.1. Every ultimately periodic set is denoted by a A-sum.Proof. ...
doi:10.1016/0304-3975(94)90044-2
fatcat:azibutcennbddpkt5snfekns7q
Syntactic Complexity of Ultimately Periodic Sets of Integers
[chapter]
2011
Lecture Notes in Computer Science
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We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. ...
We apply our results to some well studied problem: decide whether or not a brecognizable sets of integers is ultimately periodic. ...
A set X of integers is said to be b-recognizable if the language rep b (X) ⊆ A * b is a regular language accepted by some DFA. A set X ⊆ N is periodic of period p if for all n ∈ N, n ∈ X ⇔ n + p ∈ X. ...
doi:10.1007/978-3-642-21254-3_38
fatcat:emwh4zx5ebccjjzn6f6lgkapfm
Accurate Computation of Periodic Regions' Centers in the General M-Set with Integer Index Number
2010
Discrete Dynamics in Nature and Society
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One method fits for the general M-sets with integer index number, the other fits for the general M-sets with negative integer index number. ...
We primarily discuss the general M-sets with negative integer index, and analyze the relationship between the number of periodic regions' centers on the principal symmetric axis and in the principal symmetric ...
interior, then comparatively analyze the relation of periodic regions' number in general M-sets with opposite integer index number. ...
doi:10.1155/2010/653816
fatcat:56r3abvnqvgtlpujakw34ggsfq
Necessary and sufficient conditions for a sum-free set of positive integers to be ultimately periodic
2018
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We shall denote the set of sum-free sets of positive integers by S. ...
Introduction There is a natural bijection between the set of binary sequences and the set of sum-free sets of positive integers. ...
doi:10.1184/r1/6478508
fatcat:lwmgsq3qhjeqjdic4x6fdojjui
On almost periodic solutions of a class of differential equations
1959
Proceedings of the American Mathematical Society
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Considers
From this last equation we conclude that the set of e-translation integers r of e(k) is identical to the set of e-translation integers of x(k). ...
It is well-known that every almost periodic function possesses a relatively dense set of e-translation integers for each positive real number e. ...
closure of the range of 4>(t), is a uniformly continuous family of almost periodic movements in C". ...
doi:10.1090/s0002-9939-1959-0104020-2
fatcat:5a6ydjwldzefhkjbxkdbplxjuq
On Almost Periodic Solutions of a Class of Differential Equations
1959
Proceedings of the American Mathematical Society
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Considers
From this last equation we conclude that the set of e-translation integers r of e(k) is identical to the set of e-translation integers of x(k). ...
It is well-known that every almost periodic function possesses a relatively dense set of e-translation integers for each positive real number e. ...
closure of the range of 4>(t), is a uniformly continuous family of almost periodic movements in C". ...
doi:10.2307/2032898
fatcat:tp653ak5ovaoznrbrk6g6ew3pm
Linear forms and complementing sets of integers
[article]
2008
arXiv
pre-print
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If this representation function is constant, then the set B is periodic and the period of B will be bounded in terms of the diameter of the finite set phi(a_1,... ...
. + u_hx_h+vy be a linear form with nonzero integer coefficients u_1,..., u_h, v. Let A = (A_1,..., A_h) be an h-tuple of finite sets of integers and let B be an infinite set of integers. ...
For example, if A is a finite set of integers and if B is an infinite set of integers such that the pair (A, B) is complementing, then B must be a periodic set, that is, a union of congruence classes modulo ...
arXiv:0801.0001v1
fatcat:4s6jhwumkjaw3e3cmp7lwrj54a
Problems in additive number theory, II: Linear forms and complementing sets
2009
Journal de Théorie des Nombres de Bordeaux
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For example, if A is a finite set of integers and if B is an infinite set of integers such that the pair (A, B) is complementing, then B must be a periodic set, that is, a union of congruence classes modulo ...
We shall prove that the set B is periodic, and obtain an upper bound for the period of B in terms of the diameter D ψ A of the finite set ψ(A). ...
doi:10.5802/jtnb.675
fatcat:rhwowifjcncrtgc25qz6ns6dzu
Pattern Periodic Coloring of Distance Graphs
1998
Journal of combinatorial theory. Series B (Print)
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Let Z be the set of all integers. ...
The problem of determining the chromatic numbers of distance graphs on the integers has received much recent attention [1, 2, 4, 5, 11 18, 20]. The cases that |D| =1 or 2 are easy [1, 17] . ...
We say a coloring c of the set Z of integers is a pattern periodic coloring if there is an integer p, and a permutation f of the set of colors such that for every x # Z, we have c(x)= f (c(x& p)). ...
doi:10.1006/jctb.1998.1831
fatcat:ilin2a4a5zexbbyjiyvgmurixy
The 3n+l-Problem and Holomorphic Dynamics
1999
Experimental Mathematics
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A periodic point z is a point for which f n (z) = z; the period of z is the least positive integer n for which this equation holds. ...
We see that every integer sits either in the basin of attraction of a superattracting periodic orbit of integers, or it is in a wandering Fatou component. ...
doi:10.1080/10586458.1999.10504402
fatcat:ekdll3gaz5h2dh6x4sszcslv5y
Page 116 of American Mathematical Society. Proceedings of the American Mathematical Society Vol. 10, Issue 1
[page]
1959
American Mathematical Society. Proceedings of the American Mathematical Society
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MEISTERS [February
From this last equation we conclude that the set of ¢-translation integers rt of e(k) is identical to the set of €-translation integers of x(k). ...
It is well-known that every almost periodic func- tion possesses a relatively dense set of €-translation integers for each positive real number e. (Cf. [1, Paragraph 4°, p. 54]). ...
Mappings of the Interval with Finitely Many Periodic Points Have Zero Entropy
1977
Proceedings of the American Mathematical Society
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It is shown that if / is a continuous map of a closed interval into itself, and / has finitely many periodic points, then the topological entropy of / is zero. ...
Suppose that f has finitely many periodic points, and all periodic points of f are fixed points off. Let F denote the union of the set of fixed points of f and the set of endpoints of I. ...
Let n be the product of the periods of all periodic points of /. Then all periodic points of/" are fixed points of/". By Theorem B, ß(/") is the set of fixed points of /". ...
doi:10.2307/2041301
fatcat:n3dn2dkmmzagbnj4sl6ewx3kl4
Mappings of the interval with finitely many periodic points have zero entropy
1977
Proceedings of the American Mathematical Society
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It is shown that if / is a continuous map of a closed interval into itself, and / has finitely many periodic points, then the topological entropy of / is zero. ...
Suppose that f has finitely many periodic points, and all periodic points of f are fixed points off. Let F denote the union of the set of fixed points of f and the set of endpoints of I. ...
Let n be the product of the periods of all periodic points of /. Then all periodic points of/" are fixed points of/". By Theorem B, ß(/") is the set of fixed points of /". ...
doi:10.1090/s0002-9939-1977-0467841-3
fatcat:infncgt5j5dd3bylbz7ws7gkpy
Periodicity of complementing multisets
[article]
2010
arXiv
pre-print
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Let A be a finite multiset of integers. If B be a multiset such that A and B are t-complementing multisets of integers, then B is periodic. ...
Then B is periodic with period k≤ (diam(A)+1)^1/3+ϵ. ...
If B is a set such that A and B are t-complementing sets of integers with respect to ρ, then B is periodic with period log k ≤ (diam(ψ(A)) + 1) 1 3 +ε . ...
arXiv:1010.6107v2
fatcat:zmrgcxadq5golfzucwdnl3fjsm
Asymptotically Periodic Behaviour in the Dynamics of Chaotic Mappings
1987
SIAM Journal on Applied Mathematics
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Moreover almost every point is asymptotically periodic with period p, for some positive integer p. ...
We will prove that, for a chaotic mapping f belonging to a suitable class of C + functions, the set Ao(f) has Lebesgue measure zero, with A(f) a nonempty set consisting of points whose orbits do not converge ...
We set U(k)for the component of LJ{Dj;O<-j<-N(k)+N(f)-I} such that YN(k) Bd (U(k)). Let X(k) be a boundary point of UN(k) and XS(k) YN(k). ...
doi:10.1137/0147033
fatcat:7v6mynmchjgaxhejmmuyll3tzq
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