A014315 Number of permutations of squarefree monomials of degree n in n non-commutative variables that are compatible with a non-commutative monomial order (in the Groebner basis sense).

1, 2, 132, 10132883443872

Offset

1,2

Links

Table of n, a(n) for n=1..4.

Sage, Multivariate Polynomials and Polynomial Rings: Term orders.

Fritz Schwarz, Monomial orderings and Gröbner bases, ACM SIGSAM Bulletin 25(1) (1991), 10-23. [It contains the algorithm MACOT that possibly can be used to enumerate all compatible monomial orders as described in the name of the sequence. - Petros Hadjicostas, Dec 16 2019]

Wikipedia, Gröbner basis.

Wikipedia, Monomial order.

Example

For example, when n=3, 132 of the (3!)! = 720 possible permutations of xyz, xzy, yxz, yzx, zxy, zyx are compatible with a monomial order.

Crossrefs

Sequence in context: A099682 A214436 A135759 * A221468 A327911 A318965

Adjacent sequences: A014312 A014313 A014314 * A014316 A014317 A014318

Keyword

nonn,more

Author

Svante Linusson (linusson(AT)matematik.su.se)

Status

approved