6 papers
Higher -Continued Fractions and Dimers on Band Graphs
Wonwoo Kang, Yucong Lei
In this paper, we explore the theory of higher dimers on band graphs. First, we provide a combinatorial interpretation for the trace of the -deformed higher continued fraction m…
Cluster Expansions from Punctured Orbifolds
Esther Banaian, Wonwoo Kang, Elizabeth Kelley +2
We provide multiple combinatorial expansion formulas - in terms of snake graphs, labelled posets, matrices, and -walks - for elements in generalized cluster algebras associated…
Bridging the Know-Act Gap via Task-Level Autoregressive Reasoning
Jihyun Janice Ahn, Ryo Kamoi, Berk Atil +34
LLMs often generate seemingly valid answers to flawed or ill-posed inputs. This is not due to missing knowledge: under discriminative prompting, the same models can mostly identify…
Unimodality and Cluster Algebras from Surfaces
Wonwoo Kang, Kyeongjun Lee, Eunsung Lim
We prove that the rank polynomial of the lattice of order ideals of a loop fence poset is unimodal. This poset arises as the poset of join-irreducibles in the lattice of good match…
Stable Vectorization of Persistent Laplacians via Spectral Descriptors
Inkee Jung, Wonwoo Kang, Heehyun Park
Persistence images vectorize persistence diagrams into stable, finite-dimensional features. Inspired by this idea, we developed a vectorization framework for the spectral informati…
Skein relations for punctured surfaces
Esther Banaian, Wonwoo Kang, Elizabeth Kelley
We investigate skein relations in cluster algebras from punctured surfaces, extending the work of Ãanakçi-Schiffler and Musiker-Williams on unpunctured surfaces. Using a combinat…