Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Developments from Programming the Partition Method for a Power Series
  Expansion   Recently, a novel method based on coding partitions [1]-[4] has been used to
derive power series expansions to previously intractable problems. In this
method the coefficients at $k$ are determined by summing the contributions made
by each partition whose elements sum to $k$. These contributions are found by
assigning values to each element and multiplying by an appropriate multinomial
factor. This work presents a theoretical framework for the partition method for
a power series expansion. To overcome the complexity due to the contributions,
a programming methodology is created allowing more general problems to be
studied than envisaged originally. The methodology uses the bi-variate
recursive central partition (BRCP) algorithm, which is based on a tree-diagram
approach to scanning partitions. Its main advantage is that partitions are
generated in the multiplicity representation. During the development of the
theoretical framework, scanning over partitions was seen as a discrete
operation with an operator $L_{P,k}[ \cdot]$, whose summand depends on the
coefficients of the two series when the original function is written as a
pseudo-composite function. Simple modifications result in programs for other
operators of specific types of partitions such as: (1) only odd or even
elements, (2) a fixed number of elements, (3) discrete elements, (4) specific
elements and (5) those restricted by element size. Another modification
generates conjugate partitions by transposing Ferrers diagrams. The operator
approach is then applied to the generating functions for both discrete and
standard partitions. The main generalisation introduces a parameter $\omega$,
whose powers give the number of elements in the partitions while the
coefficients become polynomials in $\omega$. Finally, power series expansions
for more advanced infinite products are derived, culminating in Heine's
multi-parameter product.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph