Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumeration of standard barely set-valued tableaux of shifted shapes   A standard barely set-valued tableau of shape $\lambda$ is a filling of the
Young diagram $\lambda$ with integers $1,2,\dots,|\lambda|+1$ such that the
integers are increasing in each row and column, and every cell contains one
integer except one cell that contains two integers. Counting standard barely
set-valued tableaux is closely related to the coincidental down-degree
expectations (CDE) of lower intervals in Young's lattice. Using $q$-integral
techniques we give a formula for the number of standard barely set-valued
tableaux of arbitrary shifted shape. We show how it can be used to recover two
formulas, originally conjectured by Reiner, Tenner and Yong, and proved by
Hopkins, for numbers of standard barely set valued tableaux of particular
shifted-balanced shapes. We also prove a conjecture of Reiner, Tenner and Yong
on the CDE property of the shifted shape $(n,n-2,n-4,\dots,n-2k+2)$. Finally,
in the Appendix we raise a conjecture on an $\mathsf a;q$-analogue of the
down-degree expectation with respect to the uniform distribution for a specific
class of lower order ideals of Young's lattice.

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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-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: adap-org
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph