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pro vyhledávání: '"Keating, David"'
We study the asymptotics of bounded lecture hall tableaux. Limit shapes form when the bounds of the lecture hall tableaux go to infinity linearly in the lengths of the partitions describing the large-scale shapes of these tableaux. We prove Conjectur
Externí odkaz:
http://arxiv.org/abs/2309.15235
Autor:
Keating, David, Nicoletti, Matthew
In this article we define a generalization of the domino shuffling algorithm for tilings of the Aztec diamond to the interacting $k$-tilings recently introduced by S. Corteel, A. Gitlin, and the first author. We describe the algorithm both in terms o
Externí odkaz:
http://arxiv.org/abs/2303.09089
We study $k$-tilings ($k$-tuples of domino tilings) of the Aztec diamond of rank $m$. We assign a weight to each $k$-tiling, depending on the number of dominos of certain types and the number of "interactions" between the tilings. Employing the color
Externí odkaz:
http://arxiv.org/abs/2202.06020
Autor:
Gitlin, Andrew, Keating, David
We describe a Yang-Baxter integrable vertex model, which can be realized as a degeneration of a vertex model introduced by Aggarwal, Borodin, and Wheeler. From this vertex model, we construct a certain class of partition functions that we show are es
Externí odkaz:
http://arxiv.org/abs/2110.10273
Autor:
Keating, David
The LLT polynomials $\mathcal{L}_{\mathbf{\beta}/\mathbf{\gamma}} (X;t)$ are a family of symmetric polynomials indexed by a tuple of (possibly skew-)partitions $\mathbf{\beta}/\mathbf{\gamma}= (\beta^{(1)}/\gamma^{(1)},\ldots,\beta^{(k)}/\gamma^{(k)}
Externí odkaz:
http://arxiv.org/abs/2104.05862
We describe a novel Yang-Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are equal to the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model formalism, we gi
Externí odkaz:
http://arxiv.org/abs/2012.02376
Autor:
Keating, David
In this note we show that the area of the partitions making up an oscillating tableaux is described by a random walk on the first quadrant of $\mathbb{Z}^2$ with certain position dependent weights. We are able to recursively calculate the moments of
Externí odkaz:
http://arxiv.org/abs/2010.10093
In this paper we prove that the Euler-Lagrange equations for the limit shape for the inhomogeneous six vertex model on a cylinder have infinitely many conserved quantities.
Externí odkaz:
http://arxiv.org/abs/2004.08971
Akademický článek
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Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded lecture hall tableaux and showed that their enumeration is closely related to standar
Externí odkaz:
http://arxiv.org/abs/1905.02881