arXiv subjects

Calvin Yost-Wolff

Publications and source records attributed to Calvin Yost-Wolff.

5 recordsLinked to original sources

arXiv2026

On Jacobi sums arising from the classical doubling method

We define the notion of a non-abelian Jacobi sum $\mathcal{J}^{\mathrm{dbl}}\left(π, χ\right)$ attached to an irreducible representation $π$ of a general linear group or a classical group over a finite field and a character $χ$ of the multiplicative group of the finite field or its quadratic extension. These sums emerge in the study of the doubling method of Piatetski-Shapiro--Rallis and Lapid--Rallis. For general linear groups, we express these non-abelian Jacobi sums in terms of Kondo's non-abelian Gauss sums. For classical groups and for characters that are not conjugate-dual, we give an explicit formula for these non-abelian Jacobi sums in terms of Gauss sums attached to the Deligne--Lusztig data of the representation, and we prove that these Jacobi sums are constant on geometric Lusztig series. Our results rely on a multiplicativity result of non-abelian Jacobi sums obtained by Girsch--Zelingher.

math.NT↗

arXiv2026

Point Count of the Top-dimensional Open Positroid Variety

In [GL24], Galashin and Lam discovered that when $k$ and $n$ are coprime, the proportion of subspaces in $\mathrm{Gr}(k,n)(\mathbb{F}_q)$ that lie in the top-dimensional open positroid variety $Π_{k,n}^\circ(\mathbb{F}_q)$ is $|(\mathbb{F}_q^\times)^n|/|\mathbb{F}_{q^n}^\times|$. In this paper, I recover this point count identity by relating the split torus action on $(Π_{k,n}^\circ)_{\mathbb{F}_q}$ and an anisotropic torus action on a $\mathbb{F}_q$ rational form of $Π_{k,n}^\circ$. The main step in the point count argument and the main technical result in this paper is that cyclic rotation acts trivially on the torus-equivariant cohomology of $Π_{k,n}^\circ$ when $k$ and $n$ are coprime.

math.CO↗

arXiv2022

A Lattice Model for Super LLT Polynomials

We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock space, we prove a Cauchy identity for super LLT polynomials, simultaneously generalizing the Cauchy and dual Cauchy identities for LLT polynomials. Lastly, we construct a solvable semi-infinite Cauchy lattice model with a surprising Yang-Baxter equation and examine its connections to the Cauchy identity.

math.CO↗

arXiv2020

Rowmotion Orbits of Trapezoid Posets

Rowmotion is an invertible operator on the order ideals of a poset which has been extensively studied and is well understood for the rectangle poset. In this paper, we show that rowmotion is equivariant with respect to a bijection of Hamaker, Patrias, Pechenik and Williams between order ideals of rectangle and trapezoid posets, thereby affirming a conjecture of Hopkins that the rectangle and trapezoid posets have the same rowmotion orbit structures. Our main tools in proving this are $K$-jeu-de-taquin and (weak) $K$-Knuth equivalence of increasing tableaux. We define $almost$ $minimal$ $tableaux$ as a family of tableaux naturally arising from order ideals and show for any $λ$, the almost minimal tableaux of shape $λ$ are in different (weak) $K$-Knuth equivalence classes. We also discuss and make some progress on related conjectures of Hopkins on down-degree homomesy.

math.CO↗

arXiv2019

Extended Nestohedra and their Face Numbers

Nestohedra are a family of convex polytopes that includes permutohedra, associahedra, and graph associahedra. In this paper, we study an extension of such polytopes, called extended nestohedra. We show that these objects are indeed the boundaries of simple polytopes, answering a question of Lam and Pylyavskyy. We also study the duals of (extended) nestohedra, giving a complete characterization of isomorphisms (as simplicial complexes) between the duals of extended nestohedra and a partial characterization of isomorphisms between the duals of nestohedra and extended nestohedra. In addition, we give formulas for their $f$-, $h$-, and $γ$-vectors. This includes showing that the $f$-vectors of the extended nestohedron corresponding to a forest $F$ and the nestohedron corresponding to the line graph of $F$ are the same, as well as showing that all flag extended nestohedra have nonnegative $γ$-vectors, thus proving Gal's conjecture for a large class of flag simple polytopes. We also relate the $f$- and $h$-vectors of the nestohedra and extended nestohedra, as well as give explicit formulas for the $h$- and $γ$-vectors in terms of descent statistics for a certain class of flag extended nestohedra. Finally, we define a partial ordering on partial permutations that is a join semilattice quotient of the weak Bruhar order on the symmetric group, and such that any linear extension of the partial order provides a shelling of the dual of the stellohedron.

math.CO↗