Computes graded W-characters of Lusztig varieties over regular semisimple loci and conjectures positive unimodal coefficients for Springer-decomposed Laurent polynomials α_ψ,G^z when ψ is type-A inflated, while proving partial triangularity and Levi stability.
A proof of the Stanley–Stembridge conjecture.arXiv preprint arXiv:2410.12758
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Introduces partition division maps whose action on Schur functions yields coefficients counted by k-Yamanouchi tableaux and establishes power-sum positivity for images of elementary symmetric functions.
Deep learning identifies co-triangle-free graphs as e-positive and proves e-positivity for claw-free claw-contractible-free graphs on 10 and 11 vertices, resolving an open conjecture.
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Haiman's Conjecture and Springer's Representations
Computes graded W-characters of Lusztig varieties over regular semisimple loci and conjectures positive unimodal coefficients for Springer-decomposed Laurent polynomials α_ψ,G^z when ψ is type-A inflated, while proving partial triangularity and Levi stability.
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Partition division maps, symmetric functions and positivity
Introduces partition division maps whose action on Schur functions yields coefficients counted by k-Yamanouchi tableaux and establishes power-sum positivity for images of elementary symmetric functions.
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How to Use Deep Learning to Identify Sufficient Conditions: A Case Study on Stanley's $e$-Positivity
Deep learning identifies co-triangle-free graphs as e-positive and proves e-positivity for claw-free claw-contractible-free graphs on 10 and 11 vertices, resolving an open conjecture.