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SquareIce Enumeration
"... Starting with plane partitions possessing certain type of symmetries, many combinatorial objects came to the fore, the enumeration of which was the subject of intensive studies during the last twenty years, with of course, seminal contributions of George Andrews. Thanks to a detour through twodimen ..."
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dimensional ice models, algebraic computations cristallised to the description of a certain determinant of Cauchy type. Dividing this determinant by some straightforward factors, one is reduced to studying a symmetric polynomial in two sets of variables. We show how to separate the variables with the help
ON THE SYMMETRY OF THE PARTITION FUNCTION OF SOME SQUARE ICE MODELS
, 2009
"... We consider the partition function Z(N; x1,..., xN, y1,..., yN) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set to the special value a = exp(iπ/3). Our proof does not use ..."
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We consider the partition function Z(N; x1,..., xN, y1,..., yN) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set to the special value a = exp(iπ/3). Our proof does
Square Ice: Justication of Thermodynamic Limit and Some Properties of the Transfer Matrix
, 1996
"... We discuss extensively some properties of the wave numbers in Bethe's ansatz for the 2D ice model. Based on this, we justify thermodynamic limit, the existence of entropy, and obtain some new results about the spectral properties of the corresponding transfer matrix. Running title: Justication ..."
New enumeration formulas for alternating sign matrices and square ice partition functions
, 2012
"... The refined enumeration of alternating sign matrices (ASMs) of given order having prescribed behavior near one or more of their boundary edges has been the subject of extensive study, starting with the Refined Alternating Sign Matrix Conjecture of MillsRobbinsRumsey [25], its proof by Zeilberger ..."
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refined) enumerations. The latter case solves the problem of computing the full boundary correlation function for ASMs. The enumeration formulas are proved by deriving new representations, which are of independent interest, for the partition function of the square ice model with domain wall boundary conditions
Square Ice: Justification of Thermodynamic Limit and Some Properties of the Transfer Matrix
, 1996
"... Abstract We discuss extensively some properties of the wave numbers in Bethe's ansatz for the 2D ice model. Based on this, we justify thermodynamic limit, the existence of entropy, and obtain some new results about the spectral properties of the corresponding transfer matrix. ..."
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Abstract We discuss extensively some properties of the wave numbers in Bethe's ansatz for the 2D ice model. Based on this, we justify thermodynamic limit, the existence of entropy, and obtain some new results about the spectral properties of the corresponding transfer matrix.
Ices
"... xte last with ma f G pen e yi and the weakening rate leads to the formation of complex surface deformation and may help explain the oad reg by i 3), tec (e.g., S nk et rain ty in sufficiently highresolution images (Patel et al., 1999). Grooves typically have peaktotrough amplitudes of 200–500 m ( ..."
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(Squyres, 1981; Giese et al., 1998; Pappalardo et al., 1998) and appear to have shallow slopes with root mean squared values of 5 (Squyres, 1981). While Ganymede’s grooves tend to share these general characteristics, the tectonic deformation within the grooved terrain is complex (Fig. 1), and groove
Results 1  10
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105,066