#1
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Aztec diamond
In combinatorial mathematics, an Aztec diamond of order n consists of all squares of a square lattice whose centers (x,y) satisfy |x| + |y| ≤ n. Here n is a fixed integer, and the square lattice consists of unit squares with the origin as a vertex of 4 of them, so that both x and y are half-integers.[1] The Aztec diamond theorem states that the number of domino tilings of the Aztec diamond of order n is 2n(n+1)/2.[2] The Arctic Circle theorem says that a random tiling of a large Aztec diamond tends to be frozen outside a certain circle.[3] |
#2
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https://mathworld.wolfram.com/AztecDiamond.html
An Aztec diamond of order n is the region obtained from four staircase shapes of height n by gluing them together along the straight edges. It can therefore be defined as the union of unit squares in the plane whose edges lie on the lines of a square grid and whose centers (x,y) satisfy |x-1/2|+|y-1/2|<=n. |
#3
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Random domino tilings the Aztec diamonds, along with random lozenge tilings of a hexagon, is one of the most studied models of statistical physics. It was first introduced by Elkies-Kuperberg-Larsen-Propp in [3], and we refer to a recent survey by Johansson [4] and references therein for detailed information about it. http://math.mit.edu/~borodin/aztec.html 11 มกราคม 2021 10:06 : ข้อความนี้ถูกแก้ไขแล้ว 1 ครั้ง, ครั้งล่าสุดโดยคุณ share |
#4
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A New Simple Proof of the Aztec Diamond Theorem The Aztec diamond of order n is the union of lattice squares in the plane intersecting the square |x|+|y|<n. The Aztec diamond theorem states that the number of domino tilings of this shape is 2n(n+1)/2. It was first proved by Elkies et al. (J. Algebraic Comb. 1(2):111132, 1992). We give a new simple proof of this theorem. https://link.springer.com/article/10...373-015-1663-x |
หัวข้อคล้ายคลึงกัน | ||||
หัวข้อ | ผู้ตั้งหัวข้อ | ห้อง | คำตอบ | ข้อความล่าสุด |
Diamond # | -Math-Sci- | ข้อสอบในโรงเรียน ม.ปลาย | 24 | 16 สิงหาคม 2011 20:27 |
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