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Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end
Dynamical reflection algebra Boundary SOS model
2011/1/17
We introduce in this paper an elliptic dynamical reflection algebra describing an SOS model with reflecting end. Using factorizing Drinfel’d twist, we compute the partition function of this model with...
Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end
Dynamical reflection algebra Boundary SOS model Factorizing Drinfel’d twist
2010/12/28
We introduce in this paper an elliptic dynamical reflection algebra describing an SOS model with reflecting end. Using factorizing Drinfel’d twist, we compute the partition function of this model with...
Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
Instanton partition functions N=2 SU(N) gauge theories general surface operator W-algebra duals
2011/3/2
We write down an explicit conjecture for the instanton partition functions in 4d N = 2 SU(N) gauge theories in the presence of a certain type of surface operator.
Degree conditions for the partition of a graph into triangles and quadrilaterals
degree partition triangle quadrilateral
2011/3/1
For two positive integers r and s with r ≥ 2s−2, if G is a graph of order 3r+4s such that d(x)+d(y) ≥ 4r+4s for every xy 6∈ E(G), then G independently contains r triangles and s quadrilaterals, ...
A new representation for the partition function of the six vertex model with domain wall boundaries
Mathematical Physics (math-ph) Statistical Mechanics (cond-mat.stat-mech) Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/11
We obtain a new representation for the partition function of the six vertex model with domain wall boundaries using a functional equation recently derived by the author. This new representation is giv...
The Yao-Yao partition theorem states that given a probability measure on an affine space of dimension n having a density which is continuous and bounded away from 0, it is possible to partition the sp...
Computing the partition function for perfect matchings in a hypergraph
hypergraph perfect matching partition function permanent
2010/12/6
Given non-negative weights wS on the k-subsets S of a km-element set V , we consider the sum of the products wS1 · · ·wSm over all partitions V =S1 [ . . . [ Sm into pairwise disjoint k-subsets Si.
Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences
Andrews' spt-function Atkin's Hecke-type partition congruences
2010/11/15
New congruences are found for Andrews' smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part alpha(24z) of a certain weak Maass form M(z) of ...
On the growth of restricted integer partition functions
integer partitions asymptotic growth
2010/12/10
We study the rate of growth of p(n, S,M), the number of partitions of n whose parts all belong to S and whose multiplicities all belong to M, where S (resp. M) are given infinite sets of positive (res...
A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler’s recurrence based on the penta...
Jucys-Murphy elements for partition algebras
Partition algebras Jucys–Murphy elements central elements presentation
2010/12/3
An inductive formula is given for a family of elements which are shown to play a role in the partition algebras which is analogous to that played by classical Jucys–Murphy elements in the group algebr...
Growth partition functions for cancellative infinite monoids
Growth partition functions cancellative infinite monoids
2010/12/15
We introduce the growth partition function Z,G(t)associated with any cancellative infinite monoid with a finite generator system G. It is a power series in t whose coefficients
l...
Benford's Law For Coefficients of Modular Forms and Partition Functions
Benford's Law Coefficients of Modular Forms Partition Functions
2010/11/30
Here we prove that Benford’s law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessa...
A Unification of Two Refinements of Euler's Partition Theorem
partition Euler's partition theorem refinement bijection Bessenrodt's bijection Andrews-Olsson's theorem
2014/6/3
We obtain a unification of two refinements of Euler's partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodt's insertion algorithm for a generalization of the An...
On Stanley's Partition Function
partition function Jacobi's triple product identity hook length
2014/6/3
Stanley defined a partition function t(n) as the number of partitions λ of n such that the number of odd parts of λ is congruent to the number of odd parts of the conjugate partition λ' modulo 4. We s...