[seqfan] New or old seq: The maximum number of shift-minimal winning coalitions, "On Dedekind's problem for complete simple games"
Jonathan Post
jvospost3 at gmail.com
Tue Jan 19 04:13:49 CET 2010
1, 1, 2, 2, 3, 5, 8, 14, 23, 40, 70, 124, 221, 397, 722
Table 1. The maximum number of shift-minimal winning coalitions.
p.5 of http://arxiv.org/abs/1001.3045
On Dedekind's problem for complete simple games
Authors: Sascha Kurz, Nikolas Tautenhahn
Comments: 13 pages, 1 figure, 6 tables, submitted to ISSAC 2010
Subjects: Combinatorics (math.CO)
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.
I note that this (except for a-0) agrees with
A025591 Maximal coefficient of Product_{k<=n} (x^k+1). Number of
solutions to +- 1 +- 2 +- 3 +- ... +- n = 0 or 1.
So is this a new seq, or a comment on an old one?
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