Báo cáo toán học: " THE THREE DIMENSIONAL POLYOMINOES OF MINIMAL AREA" docx

... polyominoes. The area |c| of the polyomino c is the number of its unit squares. We denote by C n the set of all the polyominoes of area n. The perimeter P (c) of a polyomino c is the number of ... c 1 and c 2 . Putting these facts together, we see that for the values of n listed in the theorem, the sets of the minimal antecedents through the sequen...

Ngày tải lên: 07/08/2014, 06:20

... class="bi x0 y1 w1 h 2" alt =""

Ngày tải lên: 05/08/2014, 10:20

... empty matrix), then x i ≥ d, ∀i ∈ N. Proof. It is enough to show that (i) holds. The proof of (ii) is similar. We consider the following three cases. Case 1. If N > (b)=N, then b>0. It ... a nonsingular M-matrix. Hence the result follows immediately from Theorem 3.1 of [3]. Vietnam Journal of Mathematics 33:1 (2005) 91–95 The Bounds on Components of the Solution for...

Ngày tải lên: 06/08/2014, 05:20

... all three internal vertices of the two concave kites share the same labels. Proof: Since the two concave kites share the same middle vertex, there are two possible cases. Either the labels of the ... coloured white; the respon- sibility of the tenth vertex is the number of white crossings in the corresponding drawing of K 10 . The following technical Lemma is...

Ngày tải lên: 07/08/2014, 06:22

... D.MubayiandV.R¨odl, On the Tur´an number of triple systems, J. Combin. Theory (A) 100 (2002), 135–152. the electronic journal of combinatorics 10 (2003), #R18 7 3 Proof of Theorem 1 The proof consists of three ... hypergraph. The degrees of any two vertices of H differ by at most n −2. Indeed, otherwise we can delete the vertex with the smaller degree and duplicate t...

Ngày tải lên: 07/08/2014, 07:21

... the ζ matrix of S is upper-triangular. We define the Redheffer matrix R(S)ofS to be the result of replacing the first column (i.e., the column that is labeled by the 0-element) of the ζ-matrix of ... byacolumnofall1’s. By the argument of the preceding section, the permanent of R(S)isthenumberof -chains in S that contain the 0 element. The permutations of [...

Ngày tải lên: 07/08/2014, 08:22

... faithfully on a set X.Letp be the smallest prime dividing the order of G, and let M be the length of the largest orbit of the action of G on X. Then D G (X) ≤ M p−1 . Proof. With  M p−1  colors, ... identity element. The distinguishing number of the action of G on X, denoted D G (X), is the smallest r admitting a distinguishing r-coloring of X with respect to...

Ngày tải lên: 07/08/2014, 13:21

... B T C  , where A is of size m × m, B is of size m × (n − m) and C is of size (n − m) × (n − m). The sizes of blocks are shown on the margins of the matrix. Let s denote the number of 1’s in B. Then 0 ≤ ... M col (π; k). The rest of the paper is organized as follows. We present in § 2 the main result involving a criterion of j-sets, find a generating function of...

Ngày tải lên: 07/08/2014, 15:22

... ‘complexity’ of a graph decomposition D by the following parameters. The width of D is the maximum cardinality of a bag. The order of D is the number of bags. The degree of D is the maximum degree of the ... feature of the proof of Theorem 1 by Wood and Telle [51] is the use of ‘planar decompositions’ as a new tool for studying the crossing number. Pl...

Ngày tải lên: 07/08/2014, 15:22

... If K /∈ F, the surplus of the top set is 10, the surplus of a level 4 set is equal to the deficit of a level 1 set (both 6), and the surplus of a level 3 set is equal to the deficit of a level ... from the previous case that d(C) ≤ s(C)+10 and there are examples of hypercubes in which equality holds. 5. |K| = 4. The surplus of the top set is 11, the deficit of...

Ngày tải lên: 07/08/2014, 21:20