Peter L. Guo

activity

20242026

collaborators

6 papers

math.CO2026

A solution to Butler's positivity conjecture

Peter L. Guo, Mingyang Kang, Rui Xiong

Let $λ, μ, ν$ be distinct partitions such that $λ, μ \subset ν$ and $∣ ν / λ ∣ = ∣ ν / μ ∣ = 1$ . 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…

math.CO2025

Richardson tableaux and noncrossing partial matchings

Peter L. Guo

Richardson tableaux are a remarkable subfamily of standard Young tableaux introduced by Karp and Precup in order to index the irreducible components of Springer fibers equal to Ric…

math.CO2025

Hybrid Grothendieck polynomials

Peter L. Guo, Mingyang Kang, Jiaji Liu

For a skew shape $I^»/ I^¼$ , we define the hybrid Grothendieck polynomial $${G}_{Î»/Î¼}(\textbf{x};\textbf{t};\textbf{w}) =\sum_{T\in \mathrm{SVRPP}(Î»/Î¼)} \textbf{x}^{\mathrm{ircont…

math.CO2024

Schubert polynomials and patterns in permutations

Peter L. Guo, Zhuowei Lin

This paper investigates the number of supports of the Schubert polynomial $S_{w} (x)$ indexed by a permutation $w$ . This number also equals the number of lattice points in…

math.CO2024

Zero-one dual characters of flagged Weyl modules

Peter L. Guo, Zhuowei Lin, Simon C. Y. Peng

We prove a criterion of when the dual character $I ¨ _{D} (x)$ of the flagged Weyl module associated to a diagram $D$ in the grid $[n] \times [n]$ is zero-one, that is, the coefficient…