Shuffling algorithm for boxed plane partitions
نویسندگان
چکیده
منابع مشابه
Shuffling algorithm for boxed plane partitions
We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from a × b × c to (a − 1)× (b + 1)× c or (a + 1)× (b − 1)× c. Algorithmic realization of each step involves O((a+ b)c) operations. One application is an efficient perfect random sampling algorithm for uniformly distributed boxed plane partitions. ...
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We give a simple proof of a nice formula for the means and covariances of the diagonal sums of a uniformly random boxed plane parition. An a × b × c boxed plane partition is an a × b grid of integers between 0 and c inclusive, such that the numbers decrease weakly in each row and column. At the right is a 4 × 5 × 6 boxed plane parition, which for convenience we have drawn rotated 45◦. We have a...
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We introduce elliptic weights of boxed plane partitions and prove that they give rise to a generalization of MacMahon’s product formula for the number of plane partitions in a box. We then focus on the most general positive degenerations of these weights that are related to orthogonal polynomials; they form three two-dimensional families. For distributions from these families we prove two types...
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Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all plane partitions whose solid Young diagrams t inside the box). Equivalently, we describe the distribution of the three diierent orientations of lozenges in a random lozenge tiling of a large hexagon. We...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2009
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.11.008