Abstract: "A permutation group G of degree n has a natural induced action on words of length n over a finite alphabet [sigma], in which the image x[superscript g] of x under permutation g [element of] G is obtained by permuting the positions of symbols in x according to g. The key result in �...

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Bibliographische Detailangaben

1. Verfasser:	Jerrum, Mark 1955- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Edinburgh 1995
Schriftenreihe:	Laboratory for Foundations of Computer Science <Edinburgh>: LFCS report series 317
Schlagworte:	Computer software Mathematics Mathematik Combinatorial analysis Computational complexity Distribution (Probability theory)
Zusammenfassung:	Abstract: "A permutation group G of degree n has a natural induced action on words of length n over a finite alphabet [sigma], in which the image x[superscript g] of x under permutation g [element of] G is obtained by permuting the positions of symbols in x according to g. The key result in 'Pólya theory' is that the number of orbits of this action is given by an evaluation of the cycle-index polynomial P[subscript G](z₁,...,z[subscript n]) of G at the point z₁ = ... = z[subscript n] = [absolute value of sigma]. In many cases it is possible to count the number of essentially distinct instances of a combinatorial structure of a given size by evaluating the cycle-index polynomial of an appropriate symmetry group G. We address the question 'to what extent can Pólya theory be mechanised?' There are compelling complexity-theoretic reasons for believing that there is no efficient, uniform procedure for computing the cycle-index exactly, but less is known about approximate evaluation, say to within a specified relative error. The known results -- positive and negative -- will be surveyed."