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# Copyright (c) 1997-2024
# Ewgenij Gawrilow, Michael Joswig, and the polymake team
# Technische Universität Berlin, Germany
# https://polymake.org
#
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 2, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#-------------------------------------------------------------------------------
use application 'polytope';
# produce interesting g_vectors of simplicial polytopes
# Ziegler: Lectures on Polytopes, §8.6
# Example with non-unimodal f-vector:
# $p=interesting_g_vector(20,169,4203045807457);
sub interesting_g_vector(@) {
die "usage: interesting_g_vector(d,n,r)" unless scalar(@_)==3;
my ($d,$n,$r) = @_;
my $length=$d/2+1;
my $g=new Vector<Integer>($length);
$g->[0] = 1; $g->[1] = $n-$d-1+$r;
for (my $k=2; $k<$length; ++$k) {
$g->[$k] = binomial($n-$d-2+$k,$k);
}
return (new Polytope(G_VECTOR=>$g, COMBINATORIAL_DIM=>$d, SIMPLICIAL=>1));
}
# Local Variables:
# mode: perl
# c-basic-offset:3
# End:
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