×

Computing tournament sequence numbers efficiently with matrix techniques. (English) Zbl 1021.05004

Summary: We give a new, “almost explicit” formula for tournament numbers, representing them as upper left elements of the \(n\)th power of a matrix with an explicit formula for elements of the original matrix. Using this representation, we show how to compute tournament numbers in time complexity \(O(n^6)\).

MSC:

05A15 Exact enumeration problems, generating functions
15A24 Matrix equations and identities
11B83 Special sequences and polynomials
05A16 Asymptotic enumeration
PDFBibTeX XMLCite
Full Text: EuDML