Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper-triangular linear relations on multiplicities and the
  Stanley-Stembridge conjecture   In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the
Shareshian-Wachs conjecture, which links the Stanley-Stembridge conjecture in
combinatorics to the geometry of Hessenberg varieties through Tymoczko's
permutation group action on the cohomology ring of regular semisimple
Hessenberg varieties. In previous work, the authors exploited this connection
to prove a refined (graded) version of the Stanley-Stembridge conjecture in a
special case. In this manuscript, we derive a new set of linear relations
satisfied by the multiplicities of certain permutation representations in
Tymoczko's representation. We also show that these relations are
upper-triangular in an appropriate sense, and in particular, they uniquely
determine the multiplicities. As an application of these results, we prove an
inductive formula for the multiplicity coefficients corresponding to partitions
with a maximal number of parts. It follows from our formula that these
coefficients are non-negative, thus giving additional positive evidence for the
graded Stanley--Stembridge conjecture in the general case.

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The categories of this paper are: eess
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The categories of this paper are: physics
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg