Zobrazeno 1 - 10
of 28
pro vyhledávání: '"52C22, 05B45"'
Autor:
Doolittle, Joseph, McDonough, Alex
Publikováno v:
Discrete & Computational Geometry, 2024
It is broadly known that any parallelepiped tiles space by translating copies of itself along its edges. In earlier work relating to higher-dimensional sandpile groups, the second author discovered a novel construction which fragments the parallelpip
Externí odkaz:
http://arxiv.org/abs/2307.07900
This paper proves the following statement: If a convex body can form a three or fourfold translative tiling in the three-dimensional space, it must be a parallelohedron. In other words, it must be a parallelotope, a hexagonal prism, a rhombic dodecah
Externí odkaz:
http://arxiv.org/abs/2109.07116
Autor:
Przesławski, Krzysztof
Keller packings and tilings of boxes are investigated. Certain general inequality measuring a complexity of such systems is proved. A straightforward application to the unit cube tilings is given.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/1804.07499
Autor:
Zong, Chuanming
Every body knows that identical regular triangles or squares can tile the whole plane. Many people know that identical regular hexagons can tile the plane properly as well. In fact, even the bees know and use this fact! Is there any other convex doma
Externí odkaz:
http://arxiv.org/abs/1803.06610
Autor:
Németh, László
Publikováno v:
Mathematical Communications, 22 (2017) 211-225
In this article we introduce a new type of Pascal pyramids. A regular squared mosaic in the hyperbolic plane yields a $(h^2r)$-cube mosaic in space $\mathbf{H}^2\!\times\!\mathbf{R}$ and the definition of the pyramid is based on this regular mosaic.
Externí odkaz:
http://arxiv.org/abs/1701.06022
Let $d$ be a fixed positive integer and let $\epsilon>0$. It is shown that for every sufficiently large $n\geq n_0(d,\epsilon)$, the $d$-dimensional unit cube can be decomposed into exactly $n$ smaller cubes such that the ratio of the side length of
Externí odkaz:
http://arxiv.org/abs/1511.05301
Autor:
Németh, László
Publikováno v:
Beitr Algebra Geom 57 (2016) 913-927
In this paper we introduce a new type of Pascal's pyramids. The new object is called hyperbolic Pascal pyramid since the mathematical background goes back to the regular cube mosaic (cubic honeycomb) in the hyperbolic space. The definition of the hyp
Externí odkaz:
http://arxiv.org/abs/1511.02067
Publikováno v:
Journal of Computational Geometry, Vol. 7, no. 1, pp. 149-170 (2016)
We define certain natural finite sums of $n$'th roots of unity, called $G_P(n)$, that are associated to each convex integer polytope $P$, and which generalize the classical $1$-dimensional Gauss sum $G(n)$ defined over $\mathbb Z/ {n \mathbb Z}$, to
Externí odkaz:
http://arxiv.org/abs/1508.01876
Autor:
Szirmai, Jenő
$\SLR$ geometry is one of the eight 3-dimensional Thurston geometries, it can be derived from the 3-dimensional Lie group of all $2\times 2$ real matrices with determinant one. Our aim is to describe and visualize the {\it regular infinite (torus-lik
Externí odkaz:
http://arxiv.org/abs/1206.4408
Let k_1,...,k_d be positive integers, and D be a subset of [k_1]x...x[k_d], whose complement can be decomposed into disjoint sets of the form {x_1}x...x{x_{s-1}}x[k_s]x{x_{s+1}}x...x{x_d}. We conjecture that the number of elements of D can be represe
Externí odkaz:
http://arxiv.org/abs/0807.0891