2010/01/18 by Sascha Kurz, Kurz, Sascha, Nikolas Tautenhahn +1
Mathematics · #05A15 #52B20 #91B12 #94C10 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:52B20 #msc:91B12 #msc:94C10
paper · pdf · doi:10.48550/arxiv.1001.3045
13 pages, 1 figure, 6 tables, submitted to ISSAC 2010
arxiv created 2010/01/18 · arxiv updated 2010/02/26
We combine the parametric Barvinok algorithm with a generation algorithm for a finite list of suitably chosen discrete sub-cases on the enumeration of complete simple games, i.e. a special subclass of monotone Boolean functions. Recently, Freixas et al. have proven an enumeration formula for complete simple games with two types of voters. We will provide a shorter proof and an enumeration formula for complete simple games with two shift-minimal winning coalitions.