Results 1 to 10 of about 5,540 (120)
An inequality for regular near polygons [PDF]
European Journal of Combinatorics, 2005 Let $G$ denote a near-polygon distance-regular graph with diameter $d\geq 3$, valency $k$ and intersection numbers $a_1>0$, $c_2>1$. Let $ _1$ denote the second largest eigenvalue for the adjacency matrix of $G$. We show $ _1$ is at most $(k-a_1-c_2)/(c_2-1)$. We show the following are equivalent: (i) Equality is attained above; (ii) $G$ is $Q$-
Paul Terwilliger, Chih-wen Weng
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Distance Distributions in Regular Polygons [PDF]
IEEE Transactions on Vehicular Technology, 2013 This paper derives the exact cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular $\el$-sided polygon. Using this result, we obtain the closed-form probability density function (PDF) of the Euclidean distance between any arbitrary reference point and its $n$-th neighbour node ...
Khalid, Zubair, Durrani, Salman
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On monohedral tilings of a regular polygon
Aequationes mathematicae, 2023 AbstractA tiling of a topological disc by topological discs is called monohedral if all tiles are congruent. Maltby (J Comb Theory Ser A 66:40–52, 1994) characterized the monohedral tilings of a square by three topological discs. Kurusa et al. (Mediterr J Math 17:156, 2020) characterized the monohedral tilings of a circular disc by three topological ...
Basit, Bushra, Lángi, Zsolt
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Regularizing transformations of polygons
Journal of Geometry, 2017 We start with a generic n-gon \(Q_0\) with vertices \(q_{j,0}\) (\(j = 0, \dots , n-1\)) in the d-dimensional Euclidean space \({\mathbb {E}}^d\). Additionally, \(m+1\) real numbers \(u_0, \ldots , u_m \in {\mathbb {R}} \, (m < n)\) with \(\sum _{\mu = 0}^m u_\mu = 1\) are given. From these initial data we iteratively define generations of n-gons \(Q_k\
Johann Lang, Sybille Mick, Otto Röschel
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SIAM Journal on Discrete Mathematics, 2017 In this paper we study various versions of extension complexity for polygons through the study of factorization ranks of their slack matrices. In particular, we develop a new asymptotic lower bound for their nonnegative rank, shortening the gap between the current bounds, we introduce a new upper bound for their boolean rank, deriving from it some new ...
Pedro M. Silva +2 more
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A note on affinely regular polygons [PDF]
European Journal of Combinatorics, 2009 The affinely regular polygons in certain planar sets are characterized. It is also shown that the obtained results apply to cyclotomic model sets and, additionally, have consequences in the discrete tomography of these sets.
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A PROBLEM IN REGULAR POLYGONS [PDF]
School Science and Mathematics, 1918 n ...
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Pattern Recognition, 2010 This paper describes a robust regular polygon detector. Given image edges, we derive the a posteriori probability for a mixture of regular polygons, and thus the probability density function for the appearance of a set of regular polygons. Likely regular polygons can be isolated quickly by discretising and collapsing the search space into three ...
Barnes, Nick, Loy, Gareth, Shaw, David
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Equivariant Semidefinite Lifts of Regular Polygons [PDF]
Mathematics of Operations Research, 2017 Given a polytope P ⊂ ℝn, we say that P has a positive semidefinite lift (psd lift) of size d if one can express P as the projection of an affine slice of the d × d positive semidefinite cone. Such a representation allows us to solve linear optimization problems over P using a semidefinite program of size d and can be useful in practice when d is much ...
Fawzi, Hamza +2 more
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Regular ternary polygonal forms [PDF]
The Ramanujan Journal, 2020 Inspired by Dickson's classification of regular ternary quadratic forms, we prove that there are no primitive regular $m$-gonal forms when $m$ is sufficiently large. In order to do so, we construct sequences of primes that are inert in a certain quadratic field and show that they satisfy a certain inequality bounding the next prime by the product of ...
Zilong He, Ben Kane
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