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27
Loops, matchings and alternatingsign matrices
 DISCR. MATH
, 2008
"... The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes on matchings is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain classes of alternating sign matrices and lozenge ..."
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Cited by 45 (6 self)
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The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes on matchings is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain classes of alternating sign matrices and lozenge tilings of hexagons with cut off corners.
The cube recurrence
"... Keywords: cube recurrence, grove, GaleRobinson theorem ..."
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Cited by 28 (0 self)
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Keywords: cube recurrence, grove, GaleRobinson theorem
AN IZERGIN–KOREPINTYPE IDENTITY FOR THE 8VSOS MODEL, WITH APPLICATIONS TO ALTERNATING SIGN MATRICES
, 2008
"... We obtain a new expression for the partition function of the 8VSOS model with domain wall boundary conditions, which we consider to be the natural extension of the Izergin– Korepin formula for the sixvertex model. As applications, we find dynamical (in the sense of the dynamical Yang–Baxter equati ..."
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Cited by 20 (3 self)
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We obtain a new expression for the partition function of the 8VSOS model with domain wall boundary conditions, which we consider to be the natural extension of the Izergin– Korepin formula for the sixvertex model. As applications, we find dynamical (in the sense of the dynamical Yang–Baxter equation) generalizations of the enumeration and 2enumeration of alternating sign matrices.
On the Counting of Fully Packed Loop Configurations: Some new conjectures
, 2004
"... New conjectures are proposed on the numbers of FPL configurations pertaining to certain types of link patterns. Making use of the Razumov and Stroganov Ansatz, these conjectures are based on the analysis of the ground state of the TemperleyLieb chain, for periodic boundary conditions and socalled ..."
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Cited by 20 (1 self)
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New conjectures are proposed on the numbers of FPL configurations pertaining to certain types of link patterns. Making use of the Razumov and Stroganov Ansatz, these conjectures are based on the analysis of the ground state of the TemperleyLieb chain, for periodic boundary conditions and socalled "identified connectivities", up to size 2n = 22.
A periodicity theorem for the octahedron recurrence
 J. Algebraic Combin
"... In this paper we investigate a variant of the octahedron recurrence of RobbinsRumsey [8] called the bounded octahedron recurrence. It was first described by Kamnitzer and the author in [4], where it was used to relate the commutativity isomorphism for gl(n)crystals with the Schützenberger involuti ..."
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Cited by 18 (0 self)
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In this paper we investigate a variant of the octahedron recurrence of RobbinsRumsey [8] called the bounded octahedron recurrence. It was first described by Kamnitzer and the author in [4], where it was used to relate the commutativity isomorphism for gl(n)crystals with the Schützenberger involution on Young tableaux.
A Bijection between classes of Fully Packed Loops and Plane Partitions
, 2003
"... It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a ×b×c. In this note, this result is proved by constructing explicitly the bijection between these FPL and plane partitions. ..."
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Cited by 15 (8 self)
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It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a ×b×c. In this note, this result is proved by constructing explicitly the bijection between these FPL and plane partitions.
On FPL configurations with four sets of nested arches
, 2004
"... The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a, b, c, d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in te ..."
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Cited by 9 (5 self)
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The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a, b, c, d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of nonintersecting lines, the LindströmGesselViennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a, b, c, d) = 1 or 2.
Tiling groups for Wang tiles
 PROCEEDINGS OF THE 13 TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA) SIAM EDS
"... We apply tiling groups and height functions to tilings of regions in the plane by Wang tiles, which are squares with colored boundaries where the colors of shared edges must match. We define a set of tiles as unambiguous if it contains all tiles equivalent to the identity in its tiling group. For al ..."
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Cited by 7 (4 self)
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We apply tiling groups and height functions to tilings of regions in the plane by Wang tiles, which are squares with colored boundaries where the colors of shared edges must match. We define a set of tiles as unambiguous if it contains all tiles equivalent to the identity in its tiling group. For all but one set of unambiguous tiles with two colors, we give efficient algorithms that tell whether a given region with colored boundary is tileable, show how to sample random tilings, and how to calculate the number of local moves or “flips” required to transform one tiling into another. We also analyze the lattice structure of the set of tilings, and study several examples with three and four colors as well.
On the link pattern distribution of quarterturn symmetric
 FPL configurations, FPSAC 2008, Valparaiso (Chile), DMTCS proceedings
"... Abstract. We present new conjectures on the distribution of link patterns for fullypacked loop (FPL) configurations that are invariant, or almost invariant, under a quarter turn rotation, extending previous conjectures of Razumov and Stroganov and of de Gier. We prove a special case, showing that t ..."
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Abstract. We present new conjectures on the distribution of link patterns for fullypacked loop (FPL) configurations that are invariant, or almost invariant, under a quarter turn rotation, extending previous conjectures of Razumov and Stroganov and of de Gier. We prove a special case, showing that the link pattern that is conjectured to be the rarest does have the prescribed probability. As a byproduct, we get a formula for the enumeration of a new class of quasisymmetry of plane partitions. 1.