arXiv subjects

Jack Chen-An Chou

Publications and source records attributed to Jack Chen-An Chou.

5 recordsLinked to original sources

arXiv2026

Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties

Skew-symmetric matrix Schubert varieties are determinantal varieties obtained by intersecting matrix Schubert varieties with the space of skew-symmetric matrices. They are closely related to the orbit closures of the symplectic group action on the flag variety, and their torus-equivariant K-classes are the symplectic Grothendieck polynomials. We compute the Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties by giving a combinatorial formula for the degree of symplectic Grothendieck polynomials. In addition, we characterize the highest-degree homogeneous component of a symplectic Grothendieck polynomial and compute the maximal Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties.

math.CO↗

arXiv2026

Newton polytopes of fireworks Grothendieck polynomials

We show that the support of the Grothendieck polynomial $\mathfrak G_w$ of any fireworks permutation is as large as possible: a monomial appears in $\mathfrak G_w$ if and only if it divides $\mathbf x^{\mathrm{wt}(\overline{D(w)})}$ and is divisible by some monomial appearing in the Schubert polynomial $\mathfrak S_w$. Our formula implies that the homogenization of $\mathfrak G_w$ has M-convex support. We also show that for any fireworks permutation $w\in S_n$, there exists a layered permutation $π(w)\in S_n$ so that $\mathrm{supp}(\mathfrak G_{π(w)})\supseteq \mathrm{supp}(\mathfrak G_w)$.

math.CO↗

arXiv2026

Asymptotically maximal Schubitopes

We find a layered permutation $w\in S_n$ whose Schubert polynomial $\mathfrak S_w(x_1, \dots, x_n)$ has support of size asymptotically at least $n!/4^n$. This gives precise asymptotics for the growth rate of $β(n):= \max_{w\in S_n}|\mathrm{supp}(\mathfrak S_w)|$. We find a different layered permutation $w\in S_n$ whose Grothendieck polynomial has support of size asymptotically at least $n!/e^{\sqrt{2n} \cdot \ln(n)}$ and obtain more precise asymptotics for the growth rate of $β^{\mathfrak G}(n):=\max_{w\in S_n}|\mathrm{supp}(\mathfrak G_w)|$.

math.CO↗

arXiv2026

Coxeter and Schubert combinatorics of $μ$-Involutions

The variety of complete quadrics is the wonderful compactification of $GL_n/O_n$ and admits a cell decomposition into Borel orbits indexed by combinatorial objects called $μ$-involutions. We study Coxeter-theoretic properties of $μ$-involutions with results including a combinatorial description for their atoms, an exchange lemma, and transposition-like operators that characterize their Bruhat order. The corresponding orbit closures can be realized inside the flag variety. In this setting, we study the cohomology representatives of these orbits, which are, up to a scalar, the $μ$-involution Schubert polynomials. We expand $μ$-involution Schubert polynomials as a multiplicity-free sum of $ν$-involution Schubert polynomials when $ν$ refines $μ$ and provide recurrences analogous to Monk's rule for Schubert polynomials.

math.CO↗

arXiv2025

A positive combinatorial formula for the double Edelman--Greene coefficients

Lam, Lee, and Shimozono introduced the double Stanley symmetric functions in their study of the equivariant geometry of the affine Grassmannian. They proved that the associated double Edelman--Greene coefficients, the double Schur expansion coefficients of these functions, are positive, a result later refined by Anderson. They further asked for a combinatorial proof of this positivity. In this paper, we provide the first such proof, together with a combinatorial formula that manifests the finer positivity established by Anderson. Our formula is built from two combinatorial models: bumpless pipedreams and increasing chains in the Bruhat order. The proof relies on three key ingredients: a correspondence between these two models, a natural subdivision of bumpless pipedreams, and a symmetry property of increasing chains.

math.CO↗