Congruences modulo powers of 2 for a certain partition function

2013 ◽  
pp. 431-447
Author(s):  
Hei-Chi Chan ◽  
Shaun Cooper
Keyword(s):  
Partition Function ◽  
Powers Of 2

Congruences modulo powers of 2 for a certain partition function

2010 ◽  
Vol 22 (1) ◽  
pp. 101-117 ◽  
Author(s):  
Hei-Chi Chan ◽  
Shaun Cooper
Keyword(s):  
Partition Function ◽  
Powers Of 2

Congruence properties of the binary partition function

1969 ◽  
Vol 66 (2) ◽  
pp. 371-376 ◽  
Author(s):  
R. F. Churchhouse
Keyword(s):  
Partition Function ◽  
Positive Integer ◽  
Asymptotic Formula ◽  
Functional Equations ◽  
Precise Calculation ◽  
Binary Partition ◽  
Powers Of 2 ◽  
De Bruijn ◽  
Congruence Properties

We denote by b(n) the number of ways of expressing the positive integer n as the sum of powers of 2 and we call b(n) ‘the binary partition function’. This function has been studied by Euler (1), Tanturri (2–4), Mahler (5), de Bruijn(6) and Pennington (7). Euler and Tanturri were primarily concerned with deriving formulae for the precise calculation of b(n), whereas Mahler deduced an asymptotic formula for log b(n) from his analysis of the functions satisfying a certain class of functional equations. De Bruijn and Pennington extended Mahler's work and obtained more precise results.

Congruence properties of the binary partition function

1975 ◽  
Vol 78 (3) ◽  
pp. 437-442 ◽  
Author(s):  
M. D. Hirschhorn ◽  
J. H. Loxton
Keyword(s):  
Partition Function ◽  
Binary Partition ◽  
Powers Of 2 ◽  
Congruence Properties

We denote by b(n) the number of binary partitions of n, that is the number of partitions of n as the sum of powers of 2. As usual, two partitions are not considered to be distinct if they differ only in the order of their summands. It is convenient to define b(0) = 1.

scholarly journals HECKE-TYPE CONGRUENCES FOR TWO SMALLEST PARTS FUNCTIONS

2013 ◽  
Vol 09 (03) ◽  
pp. 713-728 ◽  
Author(s):  
NICKOLAS ANDERSEN
Keyword(s):  
Partition Function ◽  
Generating Functions ◽  
Hecke Operator ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Powers Of 2 ◽  
Smallest Parts Function

We prove infinitely many congruences modulo 3, 5, and powers of 2 for the overpartition function [Formula: see text] and two smallest parts functions: [Formula: see text] for overpartitions and M2spt(n) for partitions without repeated odd parts. These resemble the Hecke-type congruences found by Atkin for the partition function p(n) in 1966 and Garvan for the smallest parts function spt(n) in 2010. The proofs depend on congruences between the generating functions for [Formula: see text], [Formula: see text], and M2spt(n) and eigenforms for the half-integral weight Hecke operator T(ℓ2).

CALCULATION OF ISOTOPIC REDUCED PARTITION FUNCTION RATIO FOR AQUA COMPLEXES OF MAGNESIUM CATION

2017 ◽  
pp. 138-145
Author(s):  
A.V. BOCHKAREV ◽  
◽  
S.L. BELOPUKHOV ◽  
A.V. ZHEVNEROV ◽  
S.V. DEMIN ◽  
...  
Keyword(s):  
Partition Function ◽  
Aqua Complexes ◽  
Magnesium Cation

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

The model rotator phase

1988 ◽  
Vol 53 (5) ◽  
pp. 889-902
Author(s):  
Josef Šebek
Keyword(s):  
High Temperature ◽  
Partition Function ◽  
Conformational Flexibility ◽  
Small Probability ◽  
Crystalline Phases ◽  
Rotator Phase

It is shown that the formation of the so-called rotator phase of alkanes (one of the high temperature crystalline phases) might be connected with a partial increase of the conformational flexibility of chains. The conformations with higher number of kinks per chain, which have been neglected till now, are shown to contribute effectively to the conformational partition function. Small probability of these states given by the Boltzmann exponent is compensated by a large number of ways in which they can be distributed along the chain. The deduced features of the rotator phase seem to be in agreement with the experimentally observed properties.

TOPOLOGY OF THE GRASSMANNIAN σ MODEL ON A LATTICE

1987 ◽  
Vol 02 (08) ◽  
pp. 601-608 ◽  
Author(s):  
T. FUKAI ◽  
M. V. ATRE
Keyword(s):  
Partition Function ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Limit ◽  
Topological Term

The Grassmannian σ model with a topological term is studied on a lattice. The θ dependence of the partition function and the Wilson loop are evaluated in the strong coupling limit. The latter is shown to be independent of the area at θ = π, as in the CPN−1 model.

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