2025/02/12 by Jun, Jaiung, Mincheva, Kalina, Tolliver, Jeffrey
#05B35 #05E10 #12K10 #14T10 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2502.08810
We study tropical subrepresentations of the Boolean regular representation \mathbbB[G] of a finite group G. These are equivalent to the matroids on ground set G for which left-multiplication by each element of G is a matroid automorphism. We completely classify the tropical subrepresentations of \mathbbB[G] for rank 3. When G is an abelian group, our approach can be seen as a generalization of Golomb rulers. In doing so, we also introduce an interesting class of matroids obtained from equivalence relations on finite sets.