Báo cáo toán học: "Packing 10 or 11 Unit Squares in a Square" ppt

... electronic journal of combinatorics 10 (2003), #R8 9 Packing 10 or 11 Unit Squares in a Square Walter Stromquist Department of Mathematics Bryn Mawr College, Bryn Mawr, Pennsylvania, USA walters@chesco.com Submitted: ... ——, “Packing unit squares inside squares, II (ten unit squares) ,” DHWA Memo- randum, October 15, 1984. 6. ——, “Packing unit squares inside squar...

Ngày tải lên: 07/08/2014, 07:21

... transformed into a quadratic minimization problem and a gradient iterative procedure is employed to find the minimum. The packing diagram itself may be used to input an initial approximation for ... quickly in these cases than the “billiards” algorithm alone. 5. The new packing algorithm We describe the algorithm of Phase 1 in a form applicable for packing equal spheres in variousl...

Ngày tải lên: 07/08/2014, 06:20

... displayed in [2] show, by rotating by half a right-angle certain squares from the trivial method of packing squares, we may be able to pack one extra square, or even many extra squares. As is ... Since each lattice forms an unavoidable set, any unit square contained in S must cover at least one point from each lattice, and we remark that the C-point is both green and red. For a...

Ngày tải lên: 07/08/2014, 06:23

... ,2n −1. In this case equation (10) is equivalent to [Re1, §3] spe- cialized to a = q = 1. Again we note that exp W r (x; q) has an alternate expression in this case as an in nite product, since exp W 4 (x; ... q 2 ) −1 ∞ again by the q-binomial theorem. Furthermore, since the Coxeter diagram in the case has an edge labelled 4, there exists another additive statistic n(w), equal to 7...

Ngày tải lên: 07/08/2014, 06:20

... number of matchings in a tree In t his section, we turn to the number of matchings in a graph. This is a lso known as the Hosoya index, or the Z-index in mathematical chemistry. For a rooted tree ... shows that for all a, (a, k) ∈ B which, by Proposition 7, implies that (k, a) ∈ B. Repeating the argument by increasing k, we conclude that B = Z 2 m . the electronic journal...

Ngày tải lên: 08/08/2014, 11:20

... R. Ahlswede, H. Aydinian, and L. Khachatrian. Maximum number of constant weight vertices of the unit n-cube contained in a k-dimensional subspace. Combinatorica, 23(1):5–22, 2003. Paul Erd˝os and ... of flat spaces in a finite geometry and the uniqueness of the hamming and the macdonald codes. Journal of Combinatorial Theory, 1(1):96 104 , 1966. [5] W. Cary Huffman and Vera Pless. Fund...

Ngày tải lên: 08/08/2014, 12:22

... problems are, in general, NP-Complete as shown by Dor and Tarsi [DoTa ]. In case G = K n , the H-covering and H-packing problems have attracted much attention in the last forty years, and numerous papers ... Stanton, J.G. Kalbfleisch and R.C. Mullin, Covering and packing designs, Proc. 2 nd Chapel Hill Conf. on Combinatorial Mathematics and its applications. Univ. North Carolina, Chapel...

Ngày tải lên: 07/08/2014, 06:20

... adjacent letters in a pattern be adjacent in its occurrences in an ambient string as well. For example, an occurrence of a generalized pattern 21-3 in a permutation π = a 1 a 2 ·· a n is a subsequence a i a i+1 a j of ... #R20 8 Packing patterns into words Alexander Burstein Department of Mathematics Iowa State University Ames, IA 50 011- 2064 USA burstein@math.iast...

Ngày tải lên: 07/08/2014, 07:21

... seems to lie in the fact that a single weight b j may appear in the sum above as  b j a i  with different a i in different terms. Indeed, when the values a i are all equal, we can prove that Conjecture ... define layered patterns by analogy with layered permutations. Definition 6 A layered pattern is a strictly increasing sequence of nonincreasing seg- ments, in other words,...

Ngày tải lên: 07/08/2014, 08:22

... overlap. The problem of packing unit squares into a square was initiated by Erd˝os and Graham [2]. They prove that, for a large number s, unit squares can be packed into an s × s square so that ... contain any point in Q as its interior point, and there is a line segment L i that intersects two nonadjacent edges of S. Case-4: The center of S is inside R ∗ ,andS contains a po...

Ngày tải lên: 07/08/2014, 13:21