Triangle Bordered With Squares

... unit equilateral triangle covered by six smaller equilateral triangles Proposition 3.3. T 1 (3) ≤ 2. Proof. Consider a covering of a unit equilateral triangle T with 3 equilateral triangles T 1 ,T 2 ,T 3 each ... equilateral triangle covered by 3 smaller equilateral triangles Proposition 3.4. T 1 (5) < 9 4 . Proof. Consider a covering of a unit equilateral triangle T with one e...

Ngày tải lên: 07/08/2014, 13:21

... 2 ×2 standard subsquares containing s in E  , while the other 2m −2canbe used in any of the other 2 × 2 standard subsquares. If we again label the 2 × 2 standard subsquares with Y 1 , ,Y m in ... arrays with multiple entries in each cell. They proved a result regarding arrays with at most two entries in each cell, and we generalize their method to obtain a similar result for arrays wi...

Ngày tải lên: 07/08/2014, 13:21

... y 2 (σ) to be minimal with this property (with respect to some total order of σ (2) ). We claim that we may add or delete z 1 := se 2 (y 2 ) without ending up outside Λ 2,2 (K) and without altering ... statistical mechanics. This model deals with configurations of non-overlapping (“hard”) squares in R 2 such that the four corners of any square in the configuration coincide with the fou...

Ngày tải lên: 07/08/2014, 13:21

... K x,x with minimum degree at least x 2 . Then G contains a perfect matching. Lemma 3.4 Let x ≤ n and let P be a partial Latin square of order n with x filled columns, with one filled row α, with ... empty cells, and with all other cells empty. Then row β is completable. Lemma 3.5 Let x ≤ n and let P be a partial Latin square of order n with x filled columns, with one filled row α,...

Ngày tải lên: 07/08/2014, 15:23

... minimal with this property. Note that 1 ≤ i ≤ t r+1 . We have three cases. the electronic journal of combinatorics 16(2) (2009), #R5 15 Hard Squares with Negative Activity on Cylinders with Odd ... arXiv:0709.4120v1 [8] J. Jonsson, Hard squares with negative activity and rhombus tilings of the plane, Electronic J. Combin . 13 (2006), no. 1, #R67. [9] J. Jonsson, Hard squares on...

Ngày tải lên: 08/08/2014, 01:20

... point. We call (S, M) a bordered surface with marked points if (S, M) is none of the following: • a sphere with one or two marked points in the interior of S. • a disk with one marked point on ... can onl y be decomposed as a triangle plus a spike plus a triangle. Proof . By Lemma 1, the lower part of Figure 7 can only be obtained from gluing a spike and a triangle. For the upper...

Ngày tải lên: 08/08/2014, 14:23

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