Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 3/2017, Volume 58, Issue 1, pp. 69 - 79

We start with a generic planar n-gon $$Q_0$$ Q 0 with veritices $$q_{j,0}$$ q j , 0 ( $$j = 0, \dots , n-1$$ j = 0 , ⋯ , n - 1 ) and fixed reals $$u, v, w \in...

Geometry | Affine Iterations | 51N20 | Algebra | 51N10 | Convex and Discrete Geometry | Regular n -gons | Algebraic Geometry | Mathematics | Affine Regularization | Regular n-gons

Geometry | Affine Iterations | 51N20 | Algebra | 51N10 | Convex and Discrete Geometry | Regular n -gons | Algebraic Geometry | Mathematics | Affine Regularization | Regular n-gons

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 7149 - 7179

We prove that the planar hexagonal honeycomb is asymptotically optimal for a large class of optimal partition problems, in which the cells are assumed to be...

Logarithmic capacity | Discrete faber-krahn inequality | Cheeger constant | Honeycomb conjecture | Optimal partitions | MATHEMATICS | EIGENVALUES | logarithmic capacity | discrete Faber-Krahn inequality | INEQUALITY | honeycomb conjecture | N-GONS | Analysis of PDEs | Mathematics

Logarithmic capacity | Discrete faber-krahn inequality | Cheeger constant | Honeycomb conjecture | Optimal partitions | MATHEMATICS | EIGENVALUES | logarithmic capacity | discrete Faber-Krahn inequality | INEQUALITY | honeycomb conjecture | N-GONS | Analysis of PDEs | Mathematics

Journal Article

Functional Analysis and Its Applications, ISSN 0016-2663, 7/2015, Volume 49, Issue 3, pp. 175 - 188

We develop the spectral theory of n-periodic strictly triangular difference operators L = T -k-1 + ∑ j=1 k a i j T−j and the spectral theory of the...

Functional Analysis | moduli spaces of n -gons | Analysis | spectral theory of linear difference operators | commuting difference operators | Mathematics | frieze patterns | Gale transform | moduli spaces of n-gons | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRABILITY | HIGHER PENTAGRAM MAPS | POLYGONS | GEOMETRY | Information management

Functional Analysis | moduli spaces of n -gons | Analysis | spectral theory of linear difference operators | commuting difference operators | Mathematics | frieze patterns | Gale transform | moduli spaces of n-gons | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRABILITY | HIGHER PENTAGRAM MAPS | POLYGONS | GEOMETRY | Information management

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 05/2017, Volume 521, pp. 217 - 239

In this paper, we propose new lower and upper bounds on the linear extension complexity of regular n-gons. Our bounds are based on the equivalence between the...

Nonnegative rank | Nonnegative factorization | Boolean rank | Regular n-gons | Extension complexity | MATHEMATICS | MATHEMATICS, APPLIED | CONE | Management science

Nonnegative rank | Nonnegative factorization | Boolean rank | Regular n-gons | Extension complexity | MATHEMATICS | MATHEMATICS, APPLIED | CONE | Management science

Journal Article

Journal of Siberian Federal University - Mathematics and Physics, ISSN 1997-1397, 2014, Volume 7, Issue 2, pp. 204 - 210

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2018, Volume 32, Issue 1, pp. 352 - 371

The recent paper A Quantitative Doignon-Bell-Scarf Theorem by Aliev et al. [Combmatorica, 37 (2017), pp. 313-332] generalizes the famous Doignon-Bell-Scarf...

Integer programming | Lattice points | Helly theorem | MATHEMATICS, APPLIED | integer programming | SETS | N-GONS | lattice points | ARITHMETIC PROGRESSIONS | HELLY NUMBERS | VARIABLES | POINTS | LATTICE

Integer programming | Lattice points | Helly theorem | MATHEMATICS, APPLIED | integer programming | SETS | N-GONS | lattice points | ARITHMETIC PROGRESSIONS | HELLY NUMBERS | VARIABLES | POINTS | LATTICE

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 6/2016, Volume 182, Issue 1, pp. 51 - 72

The rolling ball theorem asserts that given a convex body $$K\subset \mathbb {R}^d$$ K ⊂ R d in Euclidean space and having a $$C^2$$ C 2 -smooth surface...

Geometry | 52A20 | 52A10 | Regular n-gons | Minimal oscillation | Blaschke rolling ball theorem | Mathematics | Convex body | Modulus of continuity | Surface normal

Geometry | 52A20 | 52A10 | Regular n-gons | Minimal oscillation | Blaschke rolling ball theorem | Mathematics | Convex body | Modulus of continuity | Surface normal

Journal Article

Journal of Geometry, ISSN 0047-2468, 07/2017, Volume 108, Issue 2, pp. 791 - 801

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00022-017-0373-3 We start...

Affine iterations in higher dimensions | polygons and regularizing iterations | regular n-gons | affine regularization

Affine iterations in higher dimensions | polygons and regularizing iterations | regular n-gons | affine regularization

Journal Article

Journal of Experimental Algorithmics (JEA), ISSN 1084-6654, 11/2016, Volume 21, Issue 1, pp. 1 - 24

While random polygon generation from a set of planar points has been widely investigated in the literature, very few works address the construction of a simple...

convex n-gons | Randomized algorithm | maximal area polygon | incremental algorithm | minimal area polygon | Incremental algorithm | Minimal area polygon | Convex n-gons | Maximal area polygon

convex n-gons | Randomized algorithm | maximal area polygon | incremental algorithm | minimal area polygon | Incremental algorithm | Minimal area polygon | Convex n-gons | Maximal area polygon

Journal Article

Discrete Mathematics, ISSN 0012-365X, 03/2015, Volume 338, Issue 3, pp. 88 - 92

In 1959, Erdős and Moser asked for the maximum number of unit distances that may occur among the vertices of a convex n-gon. Until now, the best known upper...

Unit distance | 0–1 matrix | Convex polygon | Obtuse angle property | Diagonal property | Distance matrix | 0-1 matrix | SUBMATRICES | N-GON | GRAPHS | MATHEMATICS | MAXIMUM NUMBER | MATRICES | VERTICES | Lower bounds | Reeds | Upper bounds | Mathematical analysis | Polygons

Unit distance | 0–1 matrix | Convex polygon | Obtuse angle property | Diagonal property | Distance matrix | 0-1 matrix | SUBMATRICES | N-GON | GRAPHS | MATHEMATICS | MAXIMUM NUMBER | MATRICES | VERTICES | Lower bounds | Reeds | Upper bounds | Mathematical analysis | Polygons

Journal Article

Advances in Intelligent Systems and Computing, ISSN 2194-5357, 2015, Volume 377, pp. 421 - 441

Conference Proceeding

Qualitative Theory of Dynamical Systems, ISSN 1575-5460, 2009, Volume 8, Issue 2, pp. 255 - 265

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 1/2014, Volume 30, Issue 1, pp. 71 - 81

The chromatic number of a subset of the real plane is the smallest number of colors assigned to the elements of that set such that no two points at distance 1...

Chromatic number of the plane | 05C62 | Coloring the plane | Mathematics | Engineering Design | Combinatorics | Unit distance graph | 51K99 | Primary 05C12 | 05C15 | MATHEMATICS | MAXIMUM NUMBER | DISTANCES | CONVEX N-GON | Graphs | Strip | Planes | Combinatorial analysis

Chromatic number of the plane | 05C62 | Coloring the plane | Mathematics | Engineering Design | Combinatorics | Unit distance graph | 51K99 | Primary 05C12 | 05C15 | MATHEMATICS | MAXIMUM NUMBER | DISTANCES | CONVEX N-GON | Graphs | Strip | Planes | Combinatorial analysis

Journal Article

Designs, Codes, and Cryptography, ISSN 0925-1022, 12/2012, Volume 65, Issue 3, pp. 259 - 273

We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of connected bipartite graphs and give necessary and sufficient...

Isoperimetric constant | BIBD's | Bipartite Ramanujan graphs | Eigenvalues of graphs | Generalized N-gons | Expander graphs | LDPC codes | Bipartite graphs | MINIMUM-DISTANCE | MATHEMATICS, APPLIED | FINITE GEOMETRIES | RAMANUJAN GRAPHS | EXPANDER CODES | COMPUTER SCIENCE, THEORY & METHODS | EXPLICIT CONSTRUCTION

Isoperimetric constant | BIBD's | Bipartite Ramanujan graphs | Eigenvalues of graphs | Generalized N-gons | Expander graphs | LDPC codes | Bipartite graphs | MINIMUM-DISTANCE | MATHEMATICS, APPLIED | FINITE GEOMETRIES | RAMANUJAN GRAPHS | EXPANDER CODES | COMPUTER SCIENCE, THEORY & METHODS | EXPLICIT CONSTRUCTION

Journal Article

ARCHIVE FOR MATHEMATICAL LOGIC, ISSN 1432-0665, 02/2012, Volume 51, Issue 1-2, pp. 203 - 211

Let L be a countable relational language. Baldwin asked whether there is an ab initio generic L-structure which is superstable but not omega-stable. We give a...

MATHEMATICS | Generic structures | GENERALIZED N-GONS | Superstable theories | STABILITY | omega-stable theories | LOGIC | Archives | Mathematical analysis | Mathematical logic

MATHEMATICS | Generic structures | GENERALIZED N-GONS | Superstable theories | STABILITY | omega-stable theories | LOGIC | Archives | Mathematical analysis | Mathematical logic

Journal Article

Mathematical Notes, ISSN 0001-4346, 4/2012, Volume 91, Issue 3, pp. 542 - 557

The paper is devoted to selected problems of combinatorial geometry.

associated points | n-gon | Mathematics, general | Mathematics | Erdős-Szekeres problems in combinatorial geometry | convex polygonal line (cup, cap) | Horton set

associated points | n-gon | Mathematics, general | Mathematics | Erdős-Szekeres problems in combinatorial geometry | convex polygonal line (cup, cap) | Horton set

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 1997, Volume 349, Issue 5, pp. 2069 - 2084

Journal Article

Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 02/2003, Volume 13, Issue 5, pp. 335 - 347

A bound on the minimum distance of Tanner codes / expander codes of Sipser and Spielman is obtained. Furthermore, a generalization of a decoding algorithm of...

Minimum distance | Multi-partite graphs | Expander codes | Tanner codes | Expander graphs | N-gons | Ramanujan graphs | Decoding | LDPC codes | multi-partite graphs | MATHEMATICS, APPLIED | decoding | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ERROR-CORRECTING CODES | minimum distance | expander codes | COMPUTER SCIENCE, THEORY & METHODS | expander graphs

Minimum distance | Multi-partite graphs | Expander codes | Tanner codes | Expander graphs | N-gons | Ramanujan graphs | Decoding | LDPC codes | multi-partite graphs | MATHEMATICS, APPLIED | decoding | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ERROR-CORRECTING CODES | minimum distance | expander codes | COMPUTER SCIENCE, THEORY & METHODS | expander graphs

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/1997, Volume 349, Issue 5, pp. 2069 - 2084

We define a natural generalization of generalized n-gons to the case of \Lambda-graphs (where \Lambda is a totally ordered abelian group and 0<\lambda...

MATHEMATICS | K PQ MATHEMATICS | generalized n-gons | Lambda-trees | twin trees

MATHEMATICS | K PQ MATHEMATICS | generalized n-gons | Lambda-trees | twin trees

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 6/1998, Volume 71, Issue 1, pp. 33 - 59

A C2.L-geometry is a geometry of rank 3 with elements called points, lines and quads, where residues of points are linear spaces, residues of lines are...

Geometry | Mathematics | C 2 .L-geometries | dual polar spaces | near n-gons | L-geometries | Near n-gons | Dual polar spaces | MATHEMATICS | C-2.L-geometries

Geometry | Mathematics | C 2 .L-geometries | dual polar spaces | near n-gons | L-geometries | Near n-gons | Dual polar spaces | MATHEMATICS | C-2.L-geometries

Journal Article

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