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-body problems (1) 1
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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
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
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
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
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
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
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
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
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
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
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
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
Journal Article
Mathematical Notes, ISSN 0001-4346, 4/2012, Volume 91, Issue 3, pp. 542 - 557
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
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
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
Journal Article
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