Phylogenetic analysis and homology

Abstract

Given a finite simplicial complex , we construct a chain-complex isomorphism from the simplicial chain complex of over endowed with the standard boundary operator (that maps any simplex onto the sum of all of its maximal subsets) to that same complex endowed with the incidence operator that maps any simplex to the sum of just all of its proper subsets. We also indicate why this became of interest in the context of the theory of phylogenetic diversity.