Translative packing of a convex body  by sequences of its homothetic copies

Janusz Januszewski

Displaying similar documents to “Translative packing of a convex body by sequences of its homothetic copies”

On the lower bound of packing density for convex bodies in the plane.

Doheny, Kevin R. (1995)

Beiträge zur Algebra und Geometrie

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On Convex Bodies that Permit Packings of High Density.

H. Groemer (1990)

Discrete & computational geometry

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Self-Packing of Centrally Symmetric Convex Bodies in R2 .

U. Brehm (1992)

Discrete & computational geometry

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Translative packing of a square with sequences of squares

Janusz Januszewski (2010)

Colloquium Mathematicae

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Let S be a square and let S' be a square of unit area with a diagonal parallel to a side of S. Any (finite or infinite) sequence of homothetic copies of S whose total area does not exceed 4/9 can be packed translatively into S'.

On the packing densities of superballs and other bodies.

A.M. Odlyzko, J.A. Rush, N.D. Elies (1991)

Inventiones mathematicae

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Packings of pairs with a minimum known number of quadruples

Jiří Novák (1995)

Mathematica Bohemica

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Let $E$ be an $n$ -set. The problem of packing of pairs on $E$ with a minimum number of quadruples on $E$ is settled for $n < 15$ and also for $n = 36 t + i$ , $i = 3$ , $6$ , $9$ , $12$ , where $t$ is any positive integer. In the other cases of $n$ methods have been presented for constructing the packings having a minimum known number of quadruples.

Constructing universally small subsets of a given packing index in Polish groups

Taras Banakh, Nadya Lyaskovska (2011)

Colloquium Mathematicae

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A subset of a Polish space X is called universally small if it belongs to each ccc σ-ideal with Borel base on X. Under CH in each uncountable Abelian Polish group G we construct a universally small subset A₀ ⊂ G such that |A₀ ∩ gA₀| = for each g ∈ G. For each cardinal number κ ∈ [5,⁺] the set A₀ contains a universally small subset A of G with sharp packing index $p a c k ♯ (A_{κ}) = s u p | | ⁺ : \subset {g A}_{g \in G} i s d i s j o i n t$ equal to κ.

Packing of nonuniform hypergraphs - product and sum of sizes conditions

Paweł Naroski (2009)

Discussiones Mathematicae Graph Theory

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Hypergraphs $H ₁, . . ., H_{N}$ of order n are mutually packable if one can find their edge disjoint copies in the complete hypergraph of order n. We prove that two hypergraphs are mutually packable if the product of their sizes satisfies some upper bound. Moreover we show that an arbitrary set of the hypergraphs is mutually packable if the sum of their sizes is sufficiently small.

A note on dual approximation algorithms for class constrained bin packing problems

Eduardo C. Xavier, Flàvio Keidi Miyazawa (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity $1$ , and $n$ items of $Q$ different classes, each item $e$ with class $c_{e}$ and size $s_{e}$ . The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are packed consecutively. Moreover, items in consecutive shelves must be separated by shelf divisors...