2025/08/13 by Erazo, Harold
#11A55 #11J06 #11Y65 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2508.09872
We exhibit new examples of regions of M∖ L where M and L denote the Markov and Lagrange spectra, respectively. These regions have a different nature from all known regions studied so far: they contain intruder sets associated with distinct combinatorics that trespass the region where self-replication holds. Our construction follows the usual self-replication method but replaces the standard local uniqueness condition with a more flexible and weaker property. These examples emerged from a large-scale computational search for regions of M∖ L, which indicates that many such regions with intruder sets exist. We conclude with some open problems about these new regions.