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
Examples
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.
Links
- 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.