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. The Aztec diamond theorem states that the number of domino tilings of the Aztec diamond of order n is 2n(n+1)/2. The Arctic Circle theorem says that a random tiling of a large Aztec diamond tends to be frozen outside a certain circle. It is common to color the tiles in the following fashion. First consider a checkerboard coloringof the diamond. Each tile will cover exactly one black square. Vertical tiles where the top square covers a black square,is colored in one color, and the other vertical tiles in a second. Similarly for horizontal tiles. Knuth has also defined Aztec diamonds of order n + 1/2. They are identical with the polyominoes associated with the centered square numbers. (Wikipedia).
The Aztecs: From Empire to A.I. | Podcast | Overheard at National Geographic
August 1521: Spain’s victory over the Aztec begins colonization of Mexico, but Aztec culture will survive for centuries through preservation and practice. Aztec codices—16th-century “Rosetta Stones” that preserved Aztec language and deeds—laid a foundation that scholars are building on tod
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Path to Aztec Mine Revealed | The Lost Gold of the Aztecs (Season 1)
Kevin and Chris are on a mission to find an alternate entrance into an ancient Aztec mine, in this clip from Season 1, "Spanish Death Trap." #LostGoldofTheAztecs Subscribe for more from Lost Gold of The Aztecs and other great The HISTORY Channel shows: http://histv.co/SubscribeHistoryYT
From playlist Lost Gold of The Aztecs: Official Series Playlist | History
RARE Treasure Uncovered in Mysterious Cave | The Lost Gold of the Aztecs (Season 1)
The team calls in divers to take a closer took at cave 5, and they uncover something so rare that’s totally out of the ordinary, in this clip from Season 1, "Weeping Cave." #LostGoldofTheAztecs Subscribe for more from Lost Gold of The Aztecs and other great The HISTORY Channel shows: htt
From playlist Lost Gold of The Aztecs: Official Series Playlist | History
DEADLY Aztec Weapons Unearthed | The Lost Gold of the Aztecs (Season 1)
The results of the color dye test reveal multiple confirmed tunnels. As the team continue to investigate they uncover razor sharp obsidian glass, in this clip from Season 1, "Buried Below." #LostGoldofTheAztecs Subscribe for more from Lost Gold of The Aztecs and other great The HISTORY C
From playlist Lost Gold of The Aztecs: Official Series Playlist | History
Web Originals: Ask History: What Happened to the Aztecs? | History
How and why did the once mighty Aztec Empire crumble in the 16th century? Ask History looks for answers. HISTORY®, now reaching more than 98 million homes, is the leading destination for award-winning original series and specials that connect viewers with history in an informative, immers
From playlist Web Originals | History
SKELETAL REMAINS Buried at Ancient Mine | The Lost Gold of the Aztecs (Season 1)
Kevin and Cris dig a little deeper in the ancient aztec mine after finding animal remains, in this clip from Season 1, "A Hidden Chamber." #LostGoldofTheAztecs Subscribe for more from Lost Gold of The Aztecs and other great The HISTORY Channel shows: http://histv.co/SubscribeHistoryYT F
From playlist Lost Gold of The Aztecs: Official Series Playlist | History
SACRED RELIC Unleashes New Clues | The Lost Gold of the Aztecs (Season 1)
The team calls in a trusted archeologist to examine a recently discovered sacred water stone, in this clip from Season 1, "A Grave Discovery." #LostGoldofTheAztecs Subscribe for more from Lost Gold of The Aztecs and other great The HISTORY Channel shows: http://histv.co/SubscribeHistoryY
From playlist Lost Gold of The Aztecs: Official Series Playlist | History
The ARCTIC CIRCLE THEOREM or Why do physicists play dominoes?
I only stumbled across the amazing arctic circle theorem a couple of months ago while preparing the video on Euler's pentagonal theorem. A perfect topic for a Christmas video. Before I forget, the winner of the lucky draw announced in my last video is Zachary Kaplan. He wins a copy of m
From playlist Recent videos
From playlist Contributed talks One World Symposium 2020
From playlist Contributed talks One World Symposium 2020
SECRET GOLD MINE REVEALED | Lost Gold of the Aztecs (Season 1)
The team conducts an experiment that uncovers a secret mine, in this clip from Season 1, "Explosive Discoveries." #LostGoldofTheAztecs Subscribe for more from Lost Gold of The Aztecs and other great The HISTORY Channel shows: http://histv.co/SubscribeHistoryYT Check out exclusive HISTOR
From playlist Lost Gold of The Aztecs: Official Series Playlist | History
James Propp - Conjectural Enumerations of Trimer Covers of Finite Subgraphs of the Triangular (...)
The work of Conway and Lagarias applying combinatorial group theory to packing problems suggests what we might mean by “domain-wall boundary conditions” for the trimer model on the infinite triangular lattice in which the permitted trimers are triangle trimers and three-in-a-line trimers.
From playlist Combinatorics and Arithmetic for Physics: special days
Random Tilings - Kurt Johansson
Kurt Johansson KTH November 7, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
A (2+1)-dimensional Anisotropic KPZ growth model with a smooth phase by Sunil Chhita
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From playlist Universality in random structures: Interfaces, Matrices, Sandpiles - 2019
Kurt Johansson: The Airy point process in the two-periodic Aztec diamond
Abstract: The two-periodic Aztec diamond is a dimer or random tiling model with three phases, solid, liquid and gas. The dimers form a determinantal point process with a somewhat complicated but explicit correlation kernel. I will discuss in some detail how the Airy point process can be fo
From playlist Probability and Statistics
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Sylvie Corteel: Le diamant aztèque - Cours 2
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From playlist Combinatorics
Pierre Van Moerbeke: Universality in tiling models
We consider the domino tilings of a large class of Aztec rectangles. For an appropriate scaling limit, we show that, the disordered region consists of roughly two arctic circles connected with a finite number of paths. The statistics of these paths is governed by a kernel, also found in ot
From playlist Probability and Statistics
The Sun Stone (The Calendar Stone)
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P. Di Francesco: "Triangular Ice Combinatorics"
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From playlist Asymptotic Algebraic Combinatorics 2020