129 research outputs found
Alignment of Rods and Partition of Integers
We study dynamical ordering of rods. In this process, rod alignment via
pairwise interactions competes with diffusive wiggling. Under strong diffusion,
the system is disordered, but at weak diffusion, the system is ordered. We
present an exact steady-state solution for the nonlinear and nonlocal kinetic
theory of this process. We find the Fourier transform as a function of the
order parameter, and show that Fourier modes decay exponentially with the wave
number. We also obtain the order parameter in terms of the diffusion constant.
This solution is obtained using iterated partitions of the integer numbers.Comment: 6 pages, 4 figure
Statistics of nested spiral self-avoiding loops: exact results on the square and triangular lattices
The statistics of nested spiral self-avoiding loops, which is closely related
to the partition of integers into decreasing parts, is studied on the square
and triangular lattices.Comment: Old paper, for archiving. 7 pages, 2 figures, epsf, IOP macr
On the maximal weight of -ary chain partitions with bounded parts
A -ary chain is a special type of chain partition of integers with
parts of the form for some fixed integers and . In this note,
we are interested in the maximal weight of such partitions when their parts are
distinct and cannot exceed a given bound . Characterizing the cases where
the greedy choice fails, we prove that this maximal weight is, as a function of
, asymptotically independent of , and we provide an efficient
algorithm to compute it.Comment: 17 page
Two wolstenholme's type theorems on q-binomial coefficients
In this note we prove two 'Wolstenholme-type' Theorems on q binomial coefficients, with the help of a result on partition of integers modulo prime
THE SEXTUPLE COMPLETE PARTITIONS OF INTEGERS
This paper presents the concepts of sextuple (6 – tuple) complete partitions of integers and an attempt has been given for the theorem based on the last part of sextuple complete partitions of integers
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