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Determinant Formulae for some Tiling Problems and Application to Fully Packed Loops
"... We present a number of determinant formulae for the number of tilings of various domains ..."
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Cited by 7 (4 self)
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We present a number of determinant formulae for the number of tilings of various domains
A Determinant Formula for Sums of Powers of Integers
, 2014
"... In this note, we first derive a recursive formula for the sum of powers Sk(n) = 1 k + 2k + · · · + nk, with k and n nonnegative integers. We then apply it to establish, via Cramer’s rule, an explicit determinant formula for Sk(n) involving the Bernoulli numbers and the binomial (n+ 12). Evalua ..."
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In this note, we first derive a recursive formula for the sum of powers Sk(n) = 1 k + 2k + · · · + nk, with k and n nonnegative integers. We then apply it to establish, via Cramer’s rule, an explicit determinant formula for Sk(n) involving the Bernoulli numbers and the binomial (n+ 12
Character and Determinant Formulae of Quasifinite Representation of the W1
 Algebra
"... We calculate the Kac determinant for the quasifinite representation of W1+∞ algebra up to level 8. It vanishes only when the central charge is integer. We give an algebraic construction of null states and propose the character formulae. The character of the Verma module is related to free fields in ..."
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Cited by 22 (2 self)
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We calculate the Kac determinant for the quasifinite representation of W1+∞ algebra up to level 8. It vanishes only when the central charge is integer. We give an algebraic construction of null states and propose the character formulae. The character of the Verma module is related to free fields
A Remark on the Hankel Determinant Formula for Solutions of the Toda Equation
, 2007
"... Abstract. We consider the Hankel determinant formula of the τ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the τ functions in the framework of the KP theory. Similar phenome ..."
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Cited by 2 (0 self)
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Abstract. We consider the Hankel determinant formula of the τ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the τ functions in the framework of the KP theory. Similar
On Selberg Zeta Functions, Topological Zeroes and Determinant Formulas
, 1994
"... Let X be a compact locally symmetric space form of a noncompact symmetric space G=K of rank one. So X is of the form X = \GammanG=K, where G is a real connected noncompact semisimple Lie group of real rank one, K is a maximal compact and \Gamma a cocompact and torsionfree discrete subgroup of G. We ..."
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Cited by 2 (0 self)
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regularized determinant of the sequence of topological zeroes of Z oe . Furthermore if oe = 1...
A determinant formula for the Jones polynomial of pretzel knots
 J. Knot Theory Ramifications
"... ar ..."
Generating Function Associated with the Determinant Formula for the Solutions of the Painlevé II Equation
, 2004
"... In this paper we consider a Hankel determinant formula for generic solutions of the Painlevé II equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the linear problem of which the Painlevé II equation descri ..."
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Cited by 6 (0 self)
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In this paper we consider a Hankel determinant formula for generic solutions of the Painlevé II equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the linear problem of which the Painlevé II equation
Nonlinear Integral Equations and Determinant Formulae of the Open XXZ Spin Chain
, 808
"... We derive a nonlinear integral equation for the Betheansatz solvable open XXZ spin chain of arbitrary length describing the lowest lying state with zero magnetization. For this case we show how to combine the integral representation with the known determinant formula of norms and scalar products. ..."
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Cited by 1 (1 self)
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We derive a nonlinear integral equation for the Betheansatz solvable open XXZ spin chain of arbitrary length describing the lowest lying state with zero magnetization. For this case we show how to combine the integral representation with the known determinant formula of norms and scalar products.
A Determinant Formula for a Class of Rational Solutions of Painlevé V Equation
"... We give an explicit determinant formula for a class of rational solutions of the Painlevé V equation in terms of the universal characters. 1 Introduction and Main Result It is known that six Painlevé equations are in general irreducible, namely, their solutions cannot be expressed by “classical func ..."
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Cited by 10 (4 self)
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We give an explicit determinant formula for a class of rational solutions of the Painlevé V equation in terms of the universal characters. 1 Introduction and Main Result It is known that six Painlevé equations are in general irreducible, namely, their solutions cannot be expressed by “classical
hepth/9706041 Chiral Determinant Formulae and Subsingular Vectors for the
, 1997
"... We derive conjectures for the N=2 “chiral ” determinant formulae of the Topological algebra, the Antiperiodic NS algebra, and the Periodic R algebra, corresponding to incomplete Verma modules built on chiral topological primaries, chiral and antichiral NS primaries, and Ramond ground states, respect ..."
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We derive conjectures for the N=2 “chiral ” determinant formulae of the Topological algebra, the Antiperiodic NS algebra, and the Periodic R algebra, corresponding to incomplete Verma modules built on chiral topological primaries, chiral and antichiral NS primaries, and Ramond ground states
Results 11  20
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1,086,548