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1.
Carl Pomerance 《Discrete Mathematics》1977,18(1):63-70
A tiling of the plane with polygonal tiles is said to be strict if any point common to two tiles is a vertex of both or a vertex of neither. A triangle is said to be rational if its sides have rational length. Recently R.B. Eggleton asked if it is possible to strictly tile the plane with rational triangles using precisely one triangle from each congruence class. In this paper we constructively prove the existence of such a tiling by a suitable modification of the technique suggested by Eggleton. The theory of rational points on elliptic curves, in particular, the Nagell-Lutz theorem, plays a crucial role in completing the proof. 相似文献
2.
For a convex polygonP withn sides, a ‘partitioning’ ofP inton−2 nonoverlapping triangles each of whose vertices is a vertex ofP is called a triangulation or tiling, and each triangle is a tile. Each tile has a given cost associated with it which may
differ one from another. This paper considers the problem of finding a tiling ofP such that the sum of the costs of the tiles used is a minimum, and explores the curiosity that (an abstract formulation of)
it can be cast as a linear program. Further the special structure of the linear program permits a recursive O(n
3) algorithm.
Research and reproduction of this report were partially supported by the National Science Foundation Grants MCS-8119774, MCS-7926009
and ECS-8012974; Department of Energy Contract DE-AM03-76SF00326, PA# DE-AT03-76ER72018; Office of Naval Research Contract
N00014-75-C-0267.
Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and donot necessarily reflect the views of the above sponsors. 相似文献
3.
For a self‐affine tile in $\mathbf {R}^2$ generated by an expanding matrix $A\in M_2(\mathbf {Z})$ and an integral consecutive collinear digit set ${\mathcal D}$, Leung and Lau [Trans. Amer. Math. Soc. 359 , 3337–3355 (2007).] provided a necessary and sufficient algebraic condition for it to be disklike. They also characterized the neighborhood structure of all disklike tiles in terms of the algebraic data A and ${\mathcal D}$. In this paper, we completely characterize the neighborhood structure of those non‐disklike tiles. While disklike tiles can only have either six or eight edge or vertex neighbors, non‐disklike tiles have much richer neighborhood structure. In particular, other than a finite set, a Cantor set, or a set containing a nontrivial continuum, neighbors can intersect in a union of a Cantor set and a countable set. 相似文献
4.
R. Adler T. Nowicki G. Świrszcz C. Tresser S. Winograd 《Indagationes Mathematicae》2018,29(3):831-841
This is a companion paper to Adleret al. (in press, 2015). There, we proved the existence of an absorbing invariant tile for the Error Diffusion dynamics on an acute simplex when the input is constant and “ergodic” and we discuss the geometry of this tile. Under the same assumptions we prove here that said invariant tile (a fundamental set of the lattice generated by the vertices of the simplex) which is a finite union of polytopes have the property that any union of the intersections of the tile with the Voronoï regions of the vertices is a tile for a different, explicitly defined lattice. 相似文献
5.
本文研究局部顶点李代数与顶点代数之间的关系.利用由局部顶点李代数构造顶点代数的方法,定义局部顶点李代数之间的同态,证明了同态可以唯一诱导出由局部顶点李代数构造所得到的顶点代数之间的同态. 相似文献
6.
本文研究了带有信用风险的企业债券的欧式衍生资产的定价方法,建立风险债券与无风险债券期权价格的相互关系。 相似文献
7.
Ming LI 《Frontiers of Mathematics in China》2019,14(5):881
We frst give the definition of a vertex superalgebroid. Then we construct a family of vertex superalgebras associated to vertex superalgebroids. As the main result, we find a sufficient and necessary condition that these vertex superalgebras are semi-conformal. In addition, we give a concrete example of a semi-conformal vertex superalgebra and apply our results to this superalgebra. 相似文献
8.
9.
D. Fletcher 《Discrete and Computational Geometry》2011,46(2):394-403
We give a constructive method that can decrease the number of prototiles needed to tile a space. We achieve this by exchanging
edge-to-edge matching rules for a small atlas of permitted patches. This method is illustrated with Wang tiles, and we apply
our method to present via these rules a single prototile that can only tile ℝ3 aperiodically, and a pair of square tiles that can only tile ℝ2 aperiodically. 相似文献
10.
本文首先给出复的Hilbert空间上正算子n次方根存在唯—性的构造性证明.然后讨论了关于—个正算子T的n次方根序列{m√T}的极限的三种结果. 相似文献
11.
A graph is said to be superconnected if every minimum vertex cut isolates a vertex. A graph is said to be hyperconnected if
each minimum vertex cut creates exactly two components, one of which is an isolated vertex. In this paper, we characterize
superconnected or hyperconnected vertex transitive graphs with degree 4 and 5. As a corollary, superconnected or hyperconnected
planar transitive graphs are characterized. 相似文献
12.
《数学物理学报(B辑英文版)》1999,19(4):375-381
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided. 相似文献
13.
本文研究了数字集具有严格乘积形式的自相似tile成为框架集的问题.利用Zak变换,证明了自相似tile是框架集的充要条件是其数字集D={0,1,2…,N-1}. 相似文献
14.
Keith Hubbard 《Journal of Pure and Applied Algebra》2009,213(1):109-126
We introduce the notion of vertex coalgebra, a generalization of vertex operator coalgebras. Next we investigate forms of cocommutativity, coassociativity, skew-symmetry, and an endomorphism, D∗, which hold on vertex coalgebras. The former two properties require grading. We then discuss comodule structure. We conclude by discussing instances where graded vertex coalgebras appear, particularly as related to Primc’s vertex Lie algebra and (universal) enveloping vertex algebras. 相似文献
15.
A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V (G) S is also adjacent to a vertex in V (G) S. The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G. In this paper we initiate the study of total restrained bondage in graphs. The total restrained bondage number in a graph G with no isolated vertex, is the minimum cardinality of a subset of edges E such that G E has no isolated vertex and the total restrained domination number of G E is greater than the total restrained domination number of G. We obtain several properties, exact values and bounds for the total restrained bondage number of a graph. 相似文献
16.
A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination vertex removal stable if the removal of an arbitrary vertex leaves the total domination number unchanged. On the other hand, a graph is total domination vertex removal changing if the removal of an arbitrary vertex changes the total domination number. In this paper, we study total domination vertex removal changing and stable graphs. 相似文献
17.
James W. Cannon William J. Floyd Walter R. Parry 《Discrete and Computational Geometry》2006,35(2):269-285
Let T be a regular tiling of ℝ2 which has the origin 0 as a vertex, and suppose that φ: ℝ2 → ℝ2 is a homeomorphism such that (i) φ(0)=0, (ii) the image under φ of each tile of T is a union of tiles of T, and (iii) the
images under φ
of any two tiles of T are equivalent by an orientation-preserving
isometry which takes vertices to vertices. It is proved here that there
is a subset Λ of the vertices of T such that Λ is a
lattice and φ|_Λ is a group homomorphism. The tiling φ(T) is a tiling of ℝ by polyiamonds, polyominos, or polyhexes. These
tilings occur often as expansion complexes of finite subdivision rules. The above theorem is instrumental in determining when
the tiling φ(T) is conjugate to a self-similar tiling. 相似文献
18.
《数学学报》2013,(4)
<正>Total Restrained Bondage in Graphs Nader JAFARI RAD Roslan HASNI Joanna RACZEK Lutz VOLKMANN Abstract A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V(G)-S is also adjacent to a vertex in V(G)-S.The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G.In this paper we initiate the study of 相似文献
19.
20.
《Discrete Mathematics》2022,345(9):112953
In this paper, we bring a new view about closed neighbourhood to show the vertex decomposability of graphs. Making use of the characterization of hereditary vertex decomposable graphs, we introduce a class of vertex decomposable graphs, which include some well-known classic vertex decomposable graphs such as clique-whiskered graphs and Cameron-Walker graphs. 相似文献