12 citations · 53 across the 23 of their papers we have counts for
25 papers
Separable elements and Bruhat orders
Christian Gaetz, Yibo Gao
We prove the curious fact that, in any Coxeter group, the intersection of a principal left weak order ideal with a principal right weak order ideal has a unique…
Billey-Postnikov posets, rationally smooth Schubert varieties, and Poincaré duality
Christian Gaetz, Yibo Gao
Billey-Postnikov (BP) decompositions govern when Schubert varieties decompose as bundles of smaller Schubert varieties. We further develop the theory of BP decompositions an…
Twists, Higher Dimer Covers, and Web Duality for Grassmannian Cluster Algebras
Esther Banaian, Elise Catania, Christian Gaetz +3
We study a twisted version of Fraser, Lam, and Le's higher boundary measurement map, using face weights instead of edge weights, thereby providing Laurent polynomial expansions, in…
Canonical forms of polytopes from adjoints
Christian Gaetz
Projectivizations of pointed polyhedral cones are positive geometries in the sense of Arkani-Hamed, Bai, and Lam. Their canonical forms look like $$ Ω_C(x)=\frac{A(x)}{B(x)} dx…
Poset topology, moves, and Bruhat interval polytope lattices
Christian Gaetz, Patricia Hersh
We study the poset topology of lattices arising from orientations of 1-skeleta of directionally simple polytopes, with Bruhat interval polytopes as our main example. We s…
Interlacing triangles, Schubert puzzles, and graph colorings
Christian Gaetz, Yibo Gao
We show that interlacing triangular arrays, introduced by Aggarwal-Borodin-Wheeler to study certain probability measures, can be used to compute structure constants for multiplying…
On the minimal power of in a Kazhdan-Lusztig polynomial
Christian Gaetz, Yibo Gao
For in the symmetric group, we provide an exact formula for the smallest positive power appearing in the Kazhdan-Lusztig polynomial . We also provide a t…
One-skeleton posets of Bruhat interval polytopes
Christian Gaetz
Introduced by Kodama and Williams, Bruhat interval polytopes are generalized permutohedra closely connected to the study of torus orbit closures and total positivity in Schubert va…
On automorphisms of undirected Bruhat graphs
Christian Gaetz, Yibo Gao
The (directed) Bruhat graph has the elements of the Bruhat interval as vertices, with directed edges given by multiplication by a reflection. Famously, $\hatΓ(…
Repeatable patterns and the maximum multiplicity of a generator in a reduced word
Christian Gaetz, Yibo Gao, Pakawut Jiradilok +2
We study the maximum multiplicity of a simple transposition in a reduced word for the longest permutation , a…
Products of reflections in smooth Bruhat intervals
Christian Gaetz, Ram K. Goel
A permutation is called smooth if the corresponding Schubert variety is smooth. Gilboa and Lapid prove that in the symmetric group, multiplying the reflections below a smooth eleme…
Diameters of graphs of reduced words and rank-two root subsystems
Christian Gaetz, Yibo Gao
We study the diameter of the graph of reduced words of an element in a Coxeter group whose edges correspond to applications of the Coxeter relations. We resolve conj…
Minimal elements for the limit weak order on affine Weyl groups
Christian Gaetz, Yibo Gao
The limit weak order on an affine Weyl group was introduced by Lam and Pylyavskyy in their study of total positivity for loop groups. They showed that in the case of the affine sym…
The hull metric on Coxeter groups
Christian Gaetz, Yibo Gao
We reinterpret an inequality, due originally to Sidorenko, for linear extensions of posets in terms of convex subsets of the symmetric group . We conjecture that th…
The Sperner property for -avoiding intervals in the weak order
Christian Gaetz, Katherine Tung
A well-known result of Stanley from 1980 implies that the weak order on a maximal parabolic quotient of the symmetric group has the Sperner property; this same property was r…
Balance constants for Coxeter groups
Christian Gaetz, Yibo Gao
The - Conjecture, originally formulated in 1968, is one of the best-known open problems in the theory of posets, stating that the balance constant (a quantity determined…
Self-dual intervals in the Bruhat order
Christian Gaetz, Yibo Gao
Björner-Ekedahl prove that general intervals in Bruhat order are "top-heavy", with at least as many elements in the -th corank as the -th rank. Well-known results of…
On -analogs of descent and peak polynomials
Christian Gaetz, Yibo Gao
Descent polynomials and peak polynomials, which enumerate permutations with given descent and peak sets respectively, have recently received considerable attention. We give several…
Separable elements and splittings of Weyl groups
Christian Gaetz, Yibo Gao
We continue the study of separable elements in finite Weyl groups. These elements generalize the well-studied class of separable permutations. We show that the multiplication map $…
Separable elements in Weyl groups
Christian Gaetz, Yibo Gao
We define the notion of a separable element in a finite Weyl group, generalizing the well-studied class of separable permutations. We prove that the upper and lower order ideals in…
Padded Schubert polynomials and weighted enumeration of Bruhat chains
Christian Gaetz, Yibo Gao
We prove a common generalization of the fact that the weighted number of maximal chains in the strong Bruhat order on the symmetric group is for both the code weig…
On the Sperner property for the absolute order on complex reflection groups
Christian Gaetz, Yibo Gao
Two partial orders on a reflection group, the codimension order and the prefix order, are together called the absolute order when they agree. We show that in this case the absolute…
A combinatorial duality between the weak and strong Bruhat orders
Christian Gaetz, Yibo Gao
In recent work, the authors used an order lowering operator , introduced by Stanley, to prove the strong Sperner property for the weak Bruhat order on the symmetric group.…
A combinatorial -action and the Sperner property for the weak order
Christian Gaetz, Yibo Gao
We construct a simple combinatorially-defined representation of which respects the order structure of the weak order on the symmetric group. This is used to resol…