A new lower bound for the football pool problem for $7$ matches

Laurent Habsieger

Displaying similar documents to “A new lower bound for the football pool problem for $7$ matches”

Erratum to the paper "On the disc theorem" (Ann. Polon. Math. 55 (1991), 1-10)

Cabiria Andreian Cazacu (1992)

Annales Polonici Mathematici

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Due to a technical error, part of a sentence was omitted on the top of page 8. The first line should read: “where $f_{p}^{k}$ , $p = a_{l}$ or $b_{l}$ , means the number of folds of the covering $(δ_{k}^{''}, T |, Δ_{l}^{''})$ ending at p, i.e. covering a neighbourhood of p in $a_{l} b_{l}$ without covering p itself”.

The covering number for category and partition relations on $P_{ω} (λ)$

Pierre Matet (2002)

Fundamenta Mathematicae

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We show that cov(M) is the least infinite cardinal λ such that $P_{ω} (λ)$ (the set of all finite subsets of λ ) fails to satisfy a certain natural generalization of Ramsey’s Theorem.

On Ponomarev-Systems

Ying Ge, Lin Shou (2007)

Bollettino dell'Unione Matematica Italiana

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In this paper the relations of mappings and families of subsets are investigated in Ponomarev-systems, and the following results are obtained. (1) $f$ is a sequence-covering (resp. 1-sequence-covering) mapping iff $\mathcal{P}$ is a csf -network (resp. snf -network) of $X$ for a Ponomarev-system $(f,M,X,\mathcal{P})$ ; (2) $f$ is a sequence-covering (resp. 1-sequence-covering) mapping iff every $\mathcal{P}_{n}$ is a cs-cover (resp. wsn-cover) of $X$ for a Ponomarev-system $(f,M,X,\{\mathcal{P}_{n}\})$ . As applications of these results, some relations between sequence-covering...

Secure domination and secure total domination in graphs

William F. Klostermeyer, Christina M. Mynhardt (2008)

Discussiones Mathematicae Graph Theory

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A secure (total) dominating set of a graph G = (V,E) is a (total) dominating set X ⊆ V with the property that for each u ∈ V-X, there exists x ∈ X adjacent to u such that $(X - x) \cup u$ is (total) dominating. The smallest cardinality of a secure (total) dominating set is the secure (total) domination number $γ_{s} (G) (γ_{s t} (G))$ . We characterize graphs with equal total and secure total domination numbers. We show that if G has minimum degree at least two, then $γ_{s t} (G) \leq γ_{s} (G)$ . We also show that $γ_{s t} (G)$ is at most twice the clique covering...

The nonexistence of robust codes for subsets of ω₁

David Asperó (2005)

Fundamenta Mathematicae

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Several results are presented concerning the existence or nonexistence, for a subset S of ω₁, of a real r which works as a robust code for S with respect to a given sequence $⟨ S_{α} : α < ω ₁ ⟩$ of pairwise disjoint stationary subsets of ω₁, where “robustness” of r as a code may either mean that $S \in L [r, ⟨ S *_{α} : α < ω ₁ ⟩]$ whenever each $S *_{α}$ is equal to $S_{α}$ modulo nonstationary changes, or may have the weaker meaning that $S \in L [r, ⟨ S_{α} \cap C : α < ω ₁ ⟩]$ for every club C ⊆ ω₁. Variants of the above theme are also considered which result when the requirement that...

Combinatorics of open covers (VII): Groupability

Ljubiša D. R. Kočinac, Marion Scheepers (2003)

Fundamenta Mathematicae

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We use Ramseyan partition relations to characterize: ∙ the classical covering property of Hurewicz; ∙ the covering property of Gerlits and Nagy; ∙ the combinatorial cardinal numbers and add(ℳ ). Let X be a $T_{31 / 2}$ -space. In [9] we showed that $C_{p} (X)$ has countable strong fan tightness as well as the Reznichenko property if, and only if, all finite powers of X have the Gerlits-Nagy covering property. Now we show that the following are equivalent: 1. $C_{p} (X)$ has countable fan tightness and the Reznichenko...

Lifting of homeomorphisms to branched coverings of a disk

Bronisław Wajnryb, Agnieszka Wiśniowska-Wajnryb (2012)

Fundamenta Mathematicae

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We consider a simple, possibly disconnected, d-sheeted branched covering π of a closed 2-dimensional disk D by a surface X. The isotopy classes of homeomorphisms of D which are pointwise fixed on the boundary of D and permute the branch values, form the braid group Bₙ, where n is the number of branch values. Some of these homeomorphisms can be lifted to homeomorphisms of X which fix pointwise the fiber over the base point. They form a subgroup $L^{π}$ of finite index in Bₙ. For each equivalence...

On sets of vectors of a finite vector space in which every subset of basis size is a basis

Simeon Ball (2012)

Journal of the European Mathematical Society

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It is shown that the maximum size of a set $S$ of vectors of a $k$ -dimensional vector space over $𝔽_{q}$ , with the property that every subset of size $k$ is a basis, is at most $q + 1$ , if $k \leq p$ , and at most $q + k - p$ , if $q \geq k \geq p + 1 \geq 4$ , where $q = p^{k}$ and $p$ is prime. Moreover, for $k \leq p$ , the sets $S$ of maximum size are classified, generalising Beniamino Segre’s “arc is a conic” theorem. These results have various implications. One such implication is that a $k \times (p + 2)$ matrix, with $k \leq p$ and entries from $𝔽_{p}$ , has $k$ columns which are linearly dependent....

On covering and quasi-unsplit families of curves

Laurent Bonavero, Cinzia Casagrande, Stéphane Druel (2007)

Journal of the European Mathematical Society

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Given a covering family $V$ of effective 1-cycles on a complex projective variety $X$ , we find conditions allowing one to construct a geometric quotient $q : X \to Y$ , with $q$ regular on the whole of $X$ , such that every fiber of $q$ is an equivalence class for the equivalence relation naturally defined by $V$ . Among other results, we show that on a normal and $ℚ$ -factorial projective variety $X$ with canonical singularities and $dim X \leq 4$ , every covering and quasi-unsplit family $V$ of rational curves generates a geometric...

Effective decomposition of σ-continuous Borel functions

Gabriel Debs (2014)

Fundamenta Mathematicae

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We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering ${(A ₙ)}_{n \in ω}$ of X such that $f_{| A ₙ}$ is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.

Involutions of 3-dimensional handlebodies

Andrea Pantaleoni, Riccardo Piergallini (2011)

Fundamenta Mathematicae

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We study the orientation preserving involutions of the orientable 3-dimensional handlebody $H_{g}$ , for any genus g. A complete classification of such involutions is given in terms of their fixed points.

Fermat numbers and integers of the form $a^{k} + a^{l} + p^{α}$

Yong-Gao Chen, Rui Feng, Nicolas Templier (2008)

Acta Arithmetica

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Universal acyclic resolutions for arbitrary coefficient groups

Michael Levin (2003)

Fundamenta Mathematicae

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We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n+1 and a surjective $U V^{n - 1}$ -map r: Z → X such that for every abelian group G and every integer k ≥ 2 such that $d i m_{G} X \leq k \leq n$ we have $d i m_{G} Z \leq k$ and r is G-acyclic.

Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem

Alexander Nabutovsky, Regina Rotman (2003)

Journal of the European Mathematical Society

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In this paper we present two upper bounds on the length of a shortest closed geodesic on compact Riemannian manifolds. The first upper bound depends on an upper bound on sectional curvature and an upper bound on the volume of the manifold. The second upper bound will be given in terms of a lower bound on sectional curvature, an upper bound on the diameter and a lower bound on the volume. The related questions that will also be studied are the following: given a contractible $k$ -dimensional...

The covering semigroup of invariant control systems on Lie groups

Víctor Ayala, Eyüp Kizil (2016)

Kybernetika

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It is well known that the class of invariant control systems is really relevant both from theoretical and practical point of view. This work was an attempt to connect an invariant systems on a Lie group $G$ with its covering space. Furthermore, to obtain algebraic properties of this set. Let $G$ be a Lie group with identity $e$ and $Σ \subset 𝔤$ a cone in the Lie algebra $𝔤$ of $G$ that satisfies the Lie algebra rank condition. We use a formalism developed by Sussmann, to obtain an algebraic structure on...

Lower semicontinuous envelopes in $W^{1, 1} \times L^{p}$

Ana Margarida Ribeiro, Elvira Zappale (2014)

Banach Center Publications

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The lower semicontinuity of functionals of the type $\int_{Ω} f (x, u, v, \nabla u) d x$ with respect to the $(W^{1, 1} \times L^{p})$ -weak* topology is studied. Moreover, in absence of lower semicontinuity, an integral representation in $W^{1, 1} \times L^{p}$ for the lower semicontinuous envelope is also provided.

Covering Property Axiom $C P A_{c u b e}$ and its consequences

Krzysztof Ciesielski, Janusz Pawlikowski (2003)

Fundamenta Mathematicae

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We formulate a Covering Property Axiom $C P A_{c u b e}$ , which holds in the iterated perfect set model, and show that it implies easily the following facts. (a) For every S ⊂ ℝ of cardinality continuum there exists a uniformly continuous function g: ℝ → ℝ with g[S] = [0,1]. (b) If S ⊂ ℝ is either perfectly meager or universally null then S has cardinality less than . (c) cof() = ω₁ < , i.e., the cofinality of the measure ideal is ω₁. (d) For every uniformly bounded sequence $⟨ f ₙ \in ℝ^{ℝ} ⟩_{n < ω}$ of Borel functions...

Hausdorff dimension of affine random covering sets in torus

Esa Järvenpää, Maarit Järvenpää, Henna Koivusalo, Bing Li, Ville Suomala (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We calculate the almost sure Hausdorff dimension of the random covering set ${lim sup}_{n \to \infty} (g_{n} + ξ_{n})$ in $d$ -dimensional torus $𝕋^{d}$ , where the sets $g_{n} \subset 𝕋^{d}$ are parallelepipeds, or more generally, linear images of a set with nonempty interior, and $ξ_{n} \in 𝕋^{d}$ are independent and uniformly distributed random points. The dimension formula, derived from the singular values of the linear mappings, holds provided that the sequences of the singular values are decreasing.

On the angles between certain arithmetically defined subspaces of $𝐂^{n}$

Robert Brooks (1987)

Annales de l'institut Fourier

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If ${v_{i}}$ and ${w_{j}}$ are two families of unitary bases for $C^{n}$ , and $θ$ is a fixed number, let $V^{n}$ and $W^{n}$ be subspaces of $C^{n}$ spanned by $[θ \cdot n]$ vectors in ${v_{i}}$ and ${w_{j}}$ respectively. We study the angle between $V^{n}$ and $W^{n}$ as $n$ goes to infinity. We show that when ${v_{i}}$ and ${w_{j}}$ arise in certain arithmetically defined families, the angles between $V^{n}$ and $W^{n}$ may either tend to $0$ or be bounded away from zero, depending on the behavior of an associated eigenvalue problem.

Finite-to-one continuous s-covering mappings

Alexey Ostrovsky (2007)

Fundamenta Mathematicae

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The following theorem is proved. Let f: X → Y be a finite-to-one map such that the restriction $f | f^{- 1} (S)$ is an inductively perfect map for every countable compact set S ⊂ Y. Then Y is a countable union of closed subsets $Y_{i}$ such that every restriction $f | f^{- 1} (Y_{i})$ is an inductively perfect map.

Linear combinations of partitions of unity with restricted supports

Christian Richter (2002)

Studia Mathematica

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Given a locally finite open covering of a normal space X and a Hausdorff topological vector space E, we characterize all continuous functions f: X → E which admit a representation $f = \sum_{C \in} a_{C} φ_{C}$ with $a_{C} \in E$ and a partition of unity $φ_{C} : C \in$ subordinate to . As an application, we determine the class of all functions f ∈ C(||) on the underlying space || of a Euclidean complex such that, for each polytope P ∈ , the restriction ${f |}_{P}$ attains its extrema at vertices of P. Finally, a class of extremal functions on the...

Displaying similar documents to “A new lower bound for the football pool problem for 7 matches”

Displaying similar documents to “A new lower bound for the football pool problem for $7$ matches”