## The algebraic theory of recombination spaces (2000)

Citations: | 29 - 15 self |

### BibTeX

@MISC{Stadler00thealgebraic,

author = {Peter F. Stadler and Günter P. Wagner},

title = {The algebraic theory of recombination spaces},

year = {2000}

}

### Years of Citing Articles

### OpenURL

### Abstract

A new mathematical representation is proposed for the configuration space structure induced by recombination which we called "P-structure". It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental "genotypes" the set of all recombinant genotypes obtainable from the parental ones. It is shown that this construction allows a Fourier-decomposition of fitness landscapes into a superposition of "elementary landscapes". This decomposition is analogous to the Fourier decomposition of fitness landscapes on mutation spaces. The elementary landscapes are obtained as eigenfunctions of a Laplacian operator defined for P-structures. For binary string recombination the elementary landscapes are exactly the p-spin functions (Walsh functions), i.e. the same as the elementary landscapes of the string point mutation spaces (i.e. the hypercube). This supports the notion of a strong homomorphisms between string mutation ...