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The partition function of a degenerate functional [PDF]
Communications in Mathematical Physics, 1979 The partition function of a degenerate quadratic functional is defined and studied. It is shown that Ray-Singer invariants can be interpreted as partition functions of quadratic functionals. In the case of a degenerate non-quadratic functional the semiclassical approximation to the partition function is considered.
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On Stanley's Partition Function [PDF]
The Electronic Journal of Combinatorics, 2010 Stanley defined a partition function $t(n)$ as the number of partitions $\lambda$ of $n$ such that the number of odd parts of $\lambda$ is congruent to the number of odd parts of the conjugate partition $\lambda'$ modulo $4$. We show that $t(n)$ equals the number of partitions of $n$ with an even number of hooks of even length.
William Y. C. Chen +2 more
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The Complexity of Partition Functions
Theoretical Computer Science, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrei A. Bulatov, Martin Grohe
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Partition Function for a Volume of Space
Physical Review Letters, 2023 We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The result is the exponential of the Bekenstein-Hawking entropy associated with the area of the saddle ball boundary, and ...
Ted Jacobson, Manus R. Visser
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Submodular partition functions
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amini, Omid +3 more
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A partition function estimator [PDF]
The Journal of Chemical PhysicsWe propose an estimator that allows us to calculate the value of a simple system’s partition function using finite sampling. The core idea is to neglect the contribution from high energy microstates, which are difficult to be sampled properly, and then calculate a volume correction term to compensate for this.
Ying-Chih Chiang +2 more
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Electric-magnetic Duality of Abelian Gauge Theory on the Four-torus, from the Fivebrane on T2 x T4, via their Partition Functions [PDF]
, 2014 We compute the partition function of four-dimensional abelian gauge theory on a general four-torus T4 with flat metric using Dirac quantization. In addition to an SL(4, Z) symmetry, it possesses SL(2,Z) symmetry that is electromagnetic S-duality. We show
Dolan, Louise, Sun, Yang
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On a Multiplicative Partition Function [PDF]
The Electronic Journal of Combinatorics, 2000 Let $D(s)=\sum^\infty_{m=1}a_mm^{-s}$ be the Dirichlet series generated by the infinite product $\prod^\infty_{k=2}(1-k^{-s})$. The value of $a_m$ for squarefree integers $m$ with $n$ prime factors depends only on the number $n$, and we let $f(n)$ denote this value.
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A Formula for the Partition Function That “Counts” [PDF]
Annals of Combinatorics, 2016 17 ...
Choliy, Yuriy, Sills, Andrew V.
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Spin and abelian electromagnetic duality on four-manifolds [PDF]
, 2000 We investigate the electromagnetic duality properties of an abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling constants. The
Alvarez, Marcos, Olive, David I.
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