Creativity of evolutionary program synthesis systems for bijection discovery

Determine whether evolutionary program synthesis systems using teams of large language models are sufficiently creative to discover novel combinatorial bijections.

Background

The paper investigates whether evolutionary systems such as OpenEvolve can discover mathematically meaningful bijections rather than merely reproduce familiar constructions or exploit computational shortcuts. The authors note that combinatorial bijection discovery requires explicit constructions that generalize across parameters and provide structural insight, making creativity a central unresolved capability of current large-language-model-based systems.

This question remains unresolved in the paper: OpenEvolve succeeds on one known bijection but fails to discover the 321-avoiding-permutation bijection and the area-bounce-exchanging bijection in the reported experiments. These results motivate the broader open question of whether such systems can generate genuinely novel, research-level bijections.