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Periodic sets of integers

1994
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(94)90044-2
fatcat:azibutcennbddpkt5snfekns7q
*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. ...##
###
Syntactic Complexity of Ultimately Periodic Sets of Integers
[chapter]

2011
*
Lecture Notes in Computer Science
*

We also give lower bounds for the syntactic complexity

doi:10.1007/978-3-642-21254-3_38
fatcat:emwh4zx5ebccjjzn6f6lgkapfm
*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. ...##
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Accurate Computation of Periodic Regions' Centers in the General M-Set with Integer Index Number

2010
*
Discrete Dynamics in Nature and Society
*

One method fits for the general M-

doi:10.1155/2010/653816
fatcat:56r3abvnqvgtlpujakw34ggsfq
*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. ...##
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Necessary and sufficient conditions for a sum-free set of positive integers to be ultimately periodic

2018

We shall denote the

doi:10.1184/r1/6478508
fatcat:lwmgsq3qhjeqjdic4x6fdojjui
*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*. ...##
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On almost periodic solutions of a class of differential equations

1959
*
Proceedings of the American Mathematical Society
*

Considers
From this last equation we conclude that the

doi:10.1090/s0002-9939-1959-0104020-2
fatcat:5a6ydjwldzefhkjbxkdbplxjuq
*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". ...##
###
On Almost Periodic Solutions of a Class of Differential Equations

1959
*
Proceedings of the American Mathematical Society
*

Considers
From this last equation we conclude that the

doi:10.2307/2032898
fatcat:tp653ak5ovaoznrbrk6g6ew3pm
*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". ...##
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Linear forms and complementing sets of integers
[article]

2008
*
arXiv
*
pre-print

If this representation function is constant, then the

arXiv:0801.0001v1
fatcat:4s6jhwumkjaw3e3cmp7lwrj54a
*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 ...##
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Problems in additive number theory, II: Linear forms and complementing sets

2009
*
Journal de Théorie des Nombres de Bordeaux
*

For example, if A is a finite

doi:10.5802/jtnb.675
fatcat:rhwowifjcncrtgc25qz6ns6dzu
*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). ...##
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Pattern Periodic Coloring of Distance Graphs

1998
*
Journal of combinatorial theory. Series B (Print)
*

Let Z be the

doi:10.1006/jctb.1998.1831
fatcat:ilin2a4a5zexbbyjiyvgmurixy
*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)). ...##
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The 3n+l-Problem and Holomorphic Dynamics

1999
*
Experimental Mathematics
*

A

doi:10.1080/10586458.1999.10504402
fatcat:ekdll3gaz5h2dh6x4sszcslv5y
*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. ...##
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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
*

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]). ...##
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Mappings of the Interval with Finitely Many Periodic Points Have Zero Entropy

1977
*
Proceedings of the American Mathematical Society
*

It is shown that if / is a continuous map

doi:10.2307/2041301
fatcat:n3dn2dkmmzagbnj4sl6ewx3kl4
*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*/". ...##
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Mappings of the interval with finitely many periodic points have zero entropy

1977
*
Proceedings of the American Mathematical Society
*

It is shown that if / is a continuous map

doi:10.1090/s0002-9939-1977-0467841-3
fatcat:infncgt5j5dd3bylbz7ws7gkpy
*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*/". ...##
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Periodicity of complementing multisets
[article]

2010
*
arXiv
*
pre-print

Let A be a finite multiset

arXiv:1010.6107v2
fatcat:zmrgcxadq5golfzucwdnl3fjsm
*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 . ...##
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Asymptotically Periodic Behaviour in the Dynamics of Chaotic Mappings

1987
*
SIAM Journal on Applied Mathematics
*

Moreover almost every point is asymptotically

doi:10.1137/0147033
fatcat:7v6mynmchjgaxhejmmuyll3tzq
*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). ...
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