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20242026
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math.AG2026

Equivariant multiplicities and torsion at attractive fixed points

Tao Gui, Peter L. Guo, Zhuowei Lin

Let \(X\) be a rationally smooth complex affine variety with a torus action and an attractive fixed point \(x\). Suppose that \(X\setminus\{x\}\) is \(p\)-smooth and that its integ…

math.CO2026

Palindromic real-rooted polynomials and -vectors of polytopes

Peter L. Guo, Mingyang Kang

We prove that every monic palindromic real-rooted polynomial with nonnegative integer coefficients is the -polynomial of a simplicial convex polytope. This resolves in the affir…

math.CO2026

A solution to Butler's positivity conjecture

Peter L. Guo, Mingyang Kang, Rui Xiong

Let be distinct partitions such that and . We prove Butler's positivity conjecture posed in 1994: the expansion of the Macdonald intersecti…

math.CO2026

A Lam--Postnikov--Pylyavskyy inequality for hybrid Grothendieck polynomials

Peter L. Guo, Mingyang Kang, Jiaji Liu

We prove a multivariate Lam--Postnikov--Pylyavskyy type inequality for hybrid Grothendieck polynomials, unifying and refining results for stable and dual stable Grothendieck polyno…