Displaying similar documents to “ -hypercyclic and disjoint -hypercyclic properties of binary relations over topological spaces”

A note on solvable vertex stabilizers of s -transitive graphs of prime valency

Song-Tao Guo, Hailong Hou, Yong Xu (2015)

Czechoslovak Mathematical Journal

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A graph X , with a group G of automorphisms of X , is said to be ( G , s ) -transitive, for some s 1 , if G is transitive on s -arcs but not on ( s + 1 ) -arcs. Let X be a connected ( G , s ) -transitive graph of prime valency p 5 , and G v the vertex stabilizer of a vertex v V ( X ) . Suppose that G v is solvable. Weiss (1974) proved that | G v | p ( p - 1 ) 2 . In this paper, we prove that G v ( p m ) × n for some positive integers m and n such that n div m and m p - 1 .

Tetravalent half-arc-transitive graphs of order p 2 q 2

Hailin Liu, Bengong Lou, Bo Ling (2019)

Czechoslovak Mathematical Journal

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We classify tetravalent G -half-arc-transitive graphs Γ of order p 2 q 2 , where G 𝖠𝗎𝗍 Γ and p , q are distinct odd primes. This result involves a subclass of tetravalent half-arc-transitive graphs of cube-free order.

Representation functions for binary linear forms

Fang-Gang Xue (2024)

Czechoslovak Mathematical Journal

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Let be the set of integers, 0 the set of nonnegative integers and F ( x 1 , x 2 ) = u 1 x 1 + u 2 x 2 be a binary linear form whose coefficients u 1 , u 2 are nonzero, relatively prime integers such that u 1 u 2 ± 1 and u 1 u 2 - 2 . Let f : 0 { } be any function such that the set f - 1 ( 0 ) has asymptotic density zero. In 2007, M. B. Nathanson (2007) proved that there exists a set A of integers such that r A , F ( n ) = f ( n ) for all integers n , where r A , F ( n ) = | { ( a , a ' ) : n = u 1 a + u 2 a ' : a , a ' A } | . We add the structure of difference for the binary linear form F ( x 1 , x 2 ) .

Properties of unique information

Johannes Rauh, Maik Schünemann, Jürgen Jost (2021)

Kybernetika

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We study the unique information function U I ( T : X Y ) defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of U I . We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of T , X and Y . Our results are based on a reformulation of the first...

Algebraic and topological properties of some sets in ℓ₁

Taras Banakh, Artur Bartoszewicz, Szymon Głąb, Emilia Szymonik (2012)

Colloquium Mathematicae

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For a sequence x ∈ ℓ₁∖c₀₀, one can consider the set E(x) of all subsums of the series n = 1 x ( n ) . Guthrie and Nymann proved that E(x) is one of the following types of sets: () a finite union of closed intervals; () homeomorphic to the Cantor set; homeomorphic to the set T of subsums of n = 1 b ( n ) where b(2n-1) = 3/4ⁿ and b(2n) = 2/4ⁿ. Denote by ℐ, and the sets of all sequences x ∈ ℓ₁∖c₀₀ such that E(x) has the property (ℐ), () and ( ), respectively. We show that ℐ and are strongly -algebrable and is -lineable....

A tight quantitative version of Arrow’s impossibility theorem

Nathan Keller (2012)

Journal of the European Mathematical Society

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The well-known Impossibility Theorem of Arrow asserts that any generalized social welfare function (GSWF) with at least three alternatives, which satisfies Independence of Irrelevant Alternatives (IIA) and Unanimity and is not a dictatorship, is necessarily non-transitive. In 2002, Kalai asked whether one can obtain the following quantitative version of the theorem: For any ϵ > 0 , there exists δ = δ ( ϵ ) such that if a GSWF on three alternatives satisfies the IIA condition and its probability of...

A countably cellular topological group all of whose countable subsets are closed need not be -factorizable

Mihail G. Tkachenko (2023)

Commentationes Mathematicae Universitatis Carolinae

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We construct a Hausdorff topological group G such that 1 is a precalibre of G (hence, G has countable cellularity), all countable subsets of G are closed and C -embedded in G , but G is not -factorizable. This solves Problem 8.6.3 from the book “Topological Groups and Related Structures" (2008) in the negative.

A note on a conjecture on niche hypergraphs

Pawaton Kaemawichanurat, Thiradet Jiarasuksakun (2019)

Czechoslovak Mathematical Journal

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For a digraph D , the niche hypergraph N ( D ) of D is the hypergraph having the same set of vertices as D and the set of hyperedges E ( N ( D ) ) = { e V ( D ) : | e | 2 and there exists a vertex v such that e = N D - ( v ) or e = N D + ( v ) } . A digraph is said to be acyclic if it has no directed cycle as a subdigraph. For a given hypergraph , the niche number n ^ ( ) is the smallest integer such that together with n ^ ( ) isolated vertices is the niche hypergraph of an acyclic digraph. C. Garske, M. Sonntag and H. M. Teichert (2016) conjectured that for a linear...

On n -thin dense sets in powers of topological spaces

Adam Bartoš (2016)

Commentationes Mathematicae Universitatis Carolinae

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A subset of a product of topological spaces is called n -thin if every its two distinct points differ in at least n coordinates. We generalize a construction of Gruenhage, Natkaniec, and Piotrowski, and obtain, under CH, a countable T 3 space X without isolated points such that X n contains an n -thin dense subset, but X n + 1 does not contain any n -thin dense subset. We also observe that part of the construction can be carried out under MA.

Construction methods for gaussoids

Tobias Boege, Thomas Kahle (2020)

Kybernetika

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The number of n -gaussoids is shown to be a double exponential function in n . The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing 3 -minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed 3 -minors.