arXiv subjects
Publications and source records attributed to 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 bijection preserves Monk's formula, establishing its canonical nature.
We define a moduli space of rational curves with finite-order automorphism and weighted orbits, and we prove that the combinatorics of its boundary strata are encoded by a particular polytopal complex that also captures the algebraic structure of a complex reflection group acting on the moduli space. This generalizes the situation for Losev-Manin's moduli space of curves (whose boundary strata are encoded by the permutohedron and related to the symmetric group) as well as the situation for Batyrev-Blume's moduli space of curves with involution, and it extends that work beyond the toric context.
We give bijective proofs of Monk's rule for Schubert and double Schubert polynomials computed with bumpless pipe dreams. In particular, they specialize to bijective proofs of transition and cotransition formulas of Schubert and double Schubert polynomials, which can be used to establish bijections with ordinary pipe dreams.
A stratified variety has a Kazhdan-Lusztig atlas if it can be locally modelled with Kazhdan-Lusztig varieties stratified by Schubert varieties in some Kac-Moody flag manifold via stratified isomorphisms. In this paper, we show that the partial flag manifold $G/P$ with the projected Richardson stratification has a Kazhdan-Lusztig atlas, with each chart stratified-isomorphic to a Kazhdan-Lusztig variety in the affine flag manifold of the formal loop group $\widehat{G}$ of $G$. This result generalizes that of Snider's on $Gr(k,n)$ with the positroid stratification, and is a geometric counterpart of the combinatorial correspondence between the poset of projected Richardson stratification and a certain convex set in the Bruhat order of the Weyl group of $\widehat{G}$ given by He and Lam.
A stratified manifold has a Bruhat atlas on it if it can be covered with open charts such that each chart is stratified-isomorphic to an (opposite) Bruhat cell in a (usually Kac-Moody) flag manifold. In this paper, we construct an anticanonical stratification on the wonderful compactification of the symmetric space $PSO(2n)/SO(2n-1)$ and show that the open charts are isomorphic to certain (opposite) Bruhat cells in the type $D_{n+1}$ flag manifold.
The phylogenetic tree space, introduced by Billera, Holmes, and Vogtmann, is a cone over a simplicial complex. In this short article, we construct this complex from local gluings of classical polytopes, the associahedron and the permutohedron. Its homotopy is also reinterpreted and calculated based on polytope data.