منابع مشابه
Aztec Diamonds and Baxter Permutations
Abstract We present a proof of a conjecture about the relationship between Baxter permutations and pairs of alternating sign matrices that are produced from domino tilings of Aztec diamonds. It is shown that a tiling corresponds to a pair of ASMs that are both permutation matrices if and only if the larger permutation matrix corresponds to a Baxter permutation. There has been a thriving literat...
متن کاملDomino Tilings of Aztec Diamonds, Baxter Permutations, and Snow Leopard Permutations∗
In 1992 Elkies, Kuperberg, Larsen, and Propp introduced a bijection between domino tilings of Aztec diamonds and certain pairs of alternating-sign matrices whose sizes differ by one. In this paper we first study those smaller permutations which, when viewed as matrices, are paired with the matrices for doubly alternating Baxter permutations. We call these permutations snow ∗2010 AMS Subject Cla...
متن کاملAztec Diamonds, Checkerboard Graphs, and Spanning Trees
This note derives the characteristic polynomial of a graph that represents nonjump moves in a generalized game of checkers. The number of spanning trees is also determined.
متن کاملAztec diamonds and digraphs, and Hankel determinants of Schröder numbers
The Aztec diamond of order n is a certain configuration of 2n(n+1) unit squares. We give a new proof of the fact that the number Πn of tilings of the Aztec diamond of order n with dominoes equals 2. We determine a sign-nonsingular matrix of order n(n + 1) whose determinant gives Πn. We reduce the calculation of this determinant to that of a Hankel matrix of order n whose entries are large Schrö...
متن کاملDomino Shuffling on Novak Half-Hexagons and Aztec Half-Diamonds
We explore the connections between the well-studied Aztec Diamond graphs and a new family of graphs called the Half-Hexagons, discovered by Jonathan Novak. In particular, both families of graphs have very simple domino shuffling algorithms, which turn out to be intimately related. This connection allows us to prove an “arctic parabola” theorem for the Half-Hexagons as a corollary of the Arctic ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/377