Edge partitions of the complete graph and a determinant like function

2021/02/18 by Lippold, Steven R., Staic, Mihai D., Stancu, Alin · 1 citation
#15A15 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2102.09422

Abstract

In this paper we prove the case dim(V₃)=3 of a conjecture about the exterior operad Λ^S2_Vd. For this we introduce a collection of natural involutions on the set of homogeneous cycle-free d-partitions of the complete graph K_2d, and show that these involutions correspond to the relations in Λ^S2_Vd(2d+1). When d=3 this correspondence allows us to give an explicit description of a determinant-like map and to settle the above mentioned conjecture.

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