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).

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

Offset

3,2

Links

Table of n, a(n) for n=3..9.

Max A. Alekseyev and Pavel A. Pevzner, "Multi-Break Rearrangements and Chromosomal Evolution". Theoretical Computer Science 395(2-3) (2008), pp. 193-202.

Example

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.

Crossrefs

Cf. A141347, A141348.

Sequence in context: A081681 A281940 A141774 * A018427 A275781 A199140

Adjacent sequences: A141346 A141347 A141348 * A141350 A141351 A141352

Keyword

nonn,hard,more

Author

Max Alekseyev, Jun 27 2008

Status

approved