Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Osculating Paths and Oscillating Tableaux   The combinatorics of certain osculating lattice paths is studied, and a
relationship with oscillating tableaux is obtained. More specifically, the
paths being considered have fixed start and end points on respectively the
lower and right boundaries of a rectangle in the square lattice, each path can
take only unit steps rightwards or upwards, and two different paths are
permitted to share lattice points, but not to cross or share lattice edges.
Such paths correspond to configurations of the six-vertex model of statistical
mechanics with appropriate boundary conditions, and they include cases which
correspond to alternating sign matrices and various subclasses thereof.
Referring to points of the rectangle through which no or two paths pass as
vacancies or osculations respectively, the case of primary interest is tuples
of paths with a fixed number $l$ of vacancies and osculations. It is then shown
that there exist natural bijections which map each such path tuple $P$ to a
pair $(t,\eta)$, where $\eta$ is an oscillating tableau of length $l$ (i.e., a
sequence of $l+1$ partitions, starting with the empty partition, in which the
Young diagrams of successive partitions differ by a single square), and $t$ is
a certain, compatible sequence of $l$ weakly increasing positive integers.
Furthermore, each vacancy or osculation of $P$ corresponds to a partition in
$\eta$ whose Young diagram is obtained from that of its predecessor by
respectively the addition or deletion of a square. These bijections lead to
enumeration formulae for osculating paths involving sums over oscillating
tableaux.

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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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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: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: physics