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We propose a neural exploratory framework for variational problems over graphons, i.e., symmetric measurable functions $[0,1]^2 \to [0,1]$, that arise as limits of dense graph sequences. Such problems are central to two parts of the mathematical literature: extremal graph theory, which studies graph parameter optimisat...
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...
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...
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