Author

Hongseok Yang

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Preprint Sep 2026

A Computational Obstruction to Swapping Area and Dinv: An Automata-Theoretic View of the $q,t$-Catalan Symmetry

Algebraic combinatorics often seeks bijections that explain identities between distributions object by object. Encoding combinatorial objects as words lets automata theory study such a bijection as a word-to-word computation and measure its memory, input access, and control of output order. This refines existence quest...

Jineon Baek, Byung-Hak Hwang, Joonhyun La et al. · 0 citations

Preprint Sep 2026

Bipodal optimizers in the upper-tail variational problem for regular subgraph densities

Let $H$ be a fixed $d$-regular graph with $d\ge2$, and let $t(H,\cdot)$ denote its homomorphism density. We study the upper-tail event $t(H,G(n,p))\ge r^{|E(H)|}$ for fixed $0<p<r<1$ in a dense Erd\H{o}s--R\'enyi random graph $G(n,p)$. Near the Lubetzky--Zhao replica-symmetric phase boundary and away from the exception...

Sang-Ho Lim, Seonghyuk Im, Taeyoung Kim et al. · 0 citations