Author

Jineon Baek

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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

Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman--Pereira Matrices

We establish the conjecture by de Klerk and Pasechnik (2002), claiming that the semidefinite bounds $\vartheta^{(r)}(G)(r\geq 0)$ for the stability number $\alpha(G)$ are exact at $r=\alpha(G)-1$, by exhibiting an explicit sum-of-squares certificate. This certificate allows us to recover a known characterization of the...

Jineon Baek, Luis Felipe Vargas · 0 citations