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A141349 Size of the reduced Groebner basis of the ideal < x*y(1)^vj(1)*...*y(n-2)^vj(n-2) - z(j) : j=1,2,...,m >, where vj is the j-th extreme n-breakable vector, m=A141348(n), w.r.t. the degree of x and graded reverse lexicographic ordering of the variables y(1), ..., y(n-2), z(1), ..., z(m). 2

%I #9 Jan 31 2013 12:22:27

%S 1,3,9,43,125,1117,8227

%N Size of the reduced Groebner basis of the ideal < x*y(1)^vj(1)*...*y(n-2)^vj(n-2) - z(j) : j=1,2,...,m >, where vj is the j-th extreme n-breakable vector, m=A141348(n), w.r.t. the degree of x and graded reverse lexicographic ordering of the variables y(1), ..., y(n-2), z(1), ..., z(m).

%H Max A. Alekseyev and Pavel A. Pevzner, <a href="http://dx.doi.org/10.1016/j.tcs.2008.01.013">"Multi-Break Rearrangements and Chromosomal Evolution"</a>. Theoretical Computer Science 395(2-3) (2008), pp. 193-202.

%e The Groebner basis corresponding to the set of extreme 4-breakable vectors { (1,0), (0,2) } is { y(2)^2*z(1) - y(1)*z(1), x*y(1) - z1, x*y(2)^2 - z(1) }, implying that a(4)=3.

%Y Cf. A141347, A141348.

%K nonn,hard,more

%O 3,2

%A _Max Alekseyev_, Jun 27 2008

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