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Phylogenetic analysis and homology
-
Andreas W. M. Dress
and
Yaokun Wu
Published/Copyright:
May 1, 2012
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.
Keywords: Simplicial complexes; homology; boundary operator; incidence operator; phylogenetic diversity
Received: 2009-05-25
Revised: 2010-03-07
Published Online: 2012-05-01
Published in Print: 2012-May
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Simplicial complexes;
homology;
boundary operator;
incidence operator;
phylogenetic diversity
Articles in the same Issue
- Masthead
- -variable fractals: dimension results
- Maximal function characterizations of Hardy spaces associated with magnetic Schrödinger operators
- Phylogenetic analysis and homology
- Rational homotopy type of the moduli of representations with Borel mold
- Transcendence of special values of quasi-modular forms
- Use of reproducing kernels and Berezin symbols technique in some questions of operator theory
- Infinite-dimensional supermanifolds over arbitrary base fields
- Weyl and Zariski chambers on K3 surfaces
- The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences
- Solving algebraic equations in roots of unity
