Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alternating sign matrices and totally symmetric plane partitions   We introduce a new family $\mathcal{A}_{n,k}$ of Schur positive symmetric
functions, which are defined as sums over totally symmetric plane partitions.
In the first part, we show that, for $k=1$, this family is equal to a
multivariate generating function involving $n+3$ variables of objects that
extend alternating sign matrices (ASMs), which have recently been introduced by
the authors. This establishes a new connection between ASMs and a class of
plane partitions, thereby complementing the fact that ASMs are equinumerous
with totally symmetric self-complementary plane partitions as well as with
descending plane partitions. The proof is based on a new
antisymmetrizer-to-determinant formula for which we also provide a bijective
proof. In the second part, we relate three specialisation of
$\mathcal{A}_{n,k}$ to a weighted enumeration of certain well-known classes of
column strict shifted plane partitions that generalise descending plane
partitions.

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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn