12 citations · 94 across the 39 of their papers we have counts for
39 papers
Coxeter Condorcet domains
Yibo Gao, Yulin Peng
Condorcet domains are subsets of permutations that ensure pairwise majority voting yields acyclic outcomes, and they form an active area of research at the intersection of social c…
MacNeille completions of parabolic quotients
Yibo Gao, Hanlin Xu
Alternating sign matrices (ASMs) arise as the Dedekind-MacNeille completion of the Bruhat order on the symmetric group. They enjoy fruitful combinatorial and geometric properties,…
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…
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…
Levi-spherical Schubert varieties
Yibo Gao, Reuven Hodges, Alexander Yong
We prove a short, root-system uniform, combinatorial classification of Levi-spherical Schubert varieties for any generalized flag variety of finite Lie type. We apply this to…
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…
Realizable Standard Young Tableaux
Igor Araujo, Alexander E. Black, Amanda Burcroff +3
Given two vectors and , their outer sum is given by the matrix with entries . If the entries of and are increasing and sufficiently gener…
Degrees of the stretched Kostka quasi-polynomials
Shiliang Gao, Yibo Gao
We provide a type-uniform formula for the degree of the stretched Kostka quasi-polynomial in all classical types, improving a previous result by McAllister in $\mathfr…
Electrical networks and the Grove algebra
Yibo Gao, Thomas Lam, Zixuan Xu
We study the ring of regular functions on the space of planar electrical networks, which we coin the grove algebra. This algebra is an electrical analogue of the Plücker ring studi…
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…
Balanced shifted tableaux
Jiyang Gao, Shiliang Gao, Yibo Gao
We introduce balanced shifted tableaux, as an analogue of balanced tableaux of Edelman and Greene, from the perspective of root systems of type B and C. We show that they are equin…
The Canonical Bijection Between Pipe Dreams and Bumpless Pipe Dreams
Yibo Gao, Daoji Huang
We present a direct bijection between reduced pipe dreams and reduced bumpless pipe dreams by interpreting reduced compatible sequences on bumpless pipe dreams and show that this b…
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…
Classification of Levi-spherical Schubert varieties
Yibo Gao, Reuven Hodges, Alexander Yong
A Schubert variety in the complete flag manifold is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give…
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 Rank-Generating Functions of Upho Posets
Yibo Gao, Joshua Guo, Karthik Seetharaman +1
Upper homogeneous finite type (upho) posets are a large class of partially ordered sets with the property that the principal order filter at every vertex is isomorphic to the whole…
Counting Signed Vexillary Permutations
Yibo Gao, Kaarel Hänni
We show that the number of signed permutations avoiding 1234 equals the number of signed permutations avoiding 2143 (also called vexillary signed permutations), resolving a conject…
Compatible Recurrent Identities of the Sandpile Group and Maximal Stable Configurations
Yibo Gao, Rupert Li
In the abelian sandpile model, recurrent chip configurations are of interest as they are a natural choice of coset representatives under the quotient of the reduced Laplacian. We i…
Boolean elements in the Bruhat order
Yibo Gao, Kaarel Hänni
We show that is boolean if and only if it avoids a set of Billey-Postnikov patterns, which we describe explicitly. Our proof is based on an analysis of inversion sets, and…
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…