Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hall-Littlewood symmetric functions via Yamanouchi toppling game   We define a solitary game, the Yamanouchi toppling game, on any connected
graph of n vertices. The game arises from the well-known chip-firing game when
the usual relation of equivalence defined on the set of all configurations is
replaced by a suitable partial order. The set all firing sequences of length m
that the player is allowed to perform in the Yamanouchi toppling game is shown
to be in bijection with all standard Young tableaux whose shape is a partition
of the integer m with at most n-1 parts. The set of all configurations that a
player can obtain from a starting configuration is encoded in a suitable formal
power series. When the graph is the simple path and each monomial of the series
is replaced by a suitable Schur polynomial, we prove that such a series reduces
to Hall-Littlewod symmetric polynomials. The same series provides a
combinatorial description of orthogonal polynomials when the monomials are
replaced by products of moments suitably modified.

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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex