arXiv subjects

Judy Hsin-Hui Chiang

Publications and source records attributed to Judy Hsin-Hui Chiang.

4 recordsLinked to original sources

arXiv2025

Spectrum of random-to-random shuffling in the Hecke algebra

We generalize random-to-random shuffling from a Markov chain on the symmetric group to one on the Type A Iwahori Hecke algebra, and show that its eigenvalues are polynomials in q with non-negative integer coefficients. Setting q=1 recovers results of Dieker and Saliola, whose computation of the spectrum of random-to-random in the symmetric group resolved a nearly 20 year old conjecture by Uyemura-Reyes. Our methods simplify their proofs by drawing novel connections to the Jucys-Murphy elements of the Hecke algebra, Young seminormal forms, and the Okounkov-Vershik approach to representation theory.

math.CO↗

arXiv2024

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Hexahedral (hex) meshing is a long studied topic in geometry processing with many fascinating and challenging associated problems. Hex meshes vary in complexity from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges are adjacent to exactly four hexes. Edges not satisfying this criteria are considered singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. While all hex meshes with singularities are unstructured, those with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. With this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

cs.CG↗

arXiv2024

Minimal Matchings for dP3 Cluster Variables

In previous work [LM17], Tri Lai and the second author studied a family of subgraphs of the dP3 brane tiling, called Aztec castles, whose dimer partition functions provide combinatorial formulas for cluster variables resulting from mutations of the quiver associated with the del Pezzo surface dP3. In our paper, we investigate a variant of the dP3 quiver by considering a second alphabet of variables that breaks the symmetries of the relevant recurrences. This deformation is motivated by the theory of cluster algebras with principal coefficients introduced by Fomin and Zelevinsky. Our main result gives an explicit formula extending previously known generating functions for dP3 cluster variables by using Aztec castles and constructing their associated minimal matchings.

math.CO↗

arXiv2024

Bender-Knuth involutions on linear extensions of posets

We study the permutation group $\mathcal{BK}_P$ generated by Bender-Knuth moves on linear extensions of a poset $P$, an analog of the Berenstein-Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on identifying posets $P$ for which the cactus relations hold in $\mathcal{BK}_P$. We also examine $\mathcal{BK}_P$ as a subgroup of the symmetric group $\mathfrak{S}_{\mathcal{L}(P)}$ on the set of linear extensions of $P$ with the focus on analyzing posets $P$ for which $\mathcal{BK}_P = \mathfrak{S}_{\mathcal{L}(P)}$.

math.CO↗