Macaulay2 » Documentation
Packages » ExteriorIdeals :: allHilbertSequences
next | previous | forward | backward | up | index | toc

allHilbertSequences -- compute all Hilbert sequences of quotients in an exterior algebra

Synopsis

Description

A sequence is called a Hilbert sequence whether it satisfies the Kruskal-Katona theorem in the exterior algebra E.

Example:

i1 : E=QQ[e_1..e_4,SkewCommutative=>true]

o1 = E

o1 : PolynomialRing, 4 skew commutative variable(s)
 
i2 : allHilbertSequences E

o2 = {{1, 4, 6, 4, 1}, {1, 4, 6, 4, 0}, {1, 4, 6, 3, 0}, {1, 4, 6, 2, 0}, {1,
     ------------------------------------------------------------------------
     4, 6, 1, 0}, {1, 4, 6, 0, 0}, {1, 4, 5, 2, 0}, {1, 4, 5, 1, 0}, {1, 4,
     ------------------------------------------------------------------------
     5, 0, 0}, {1, 4, 4, 1, 0}, {1, 4, 4, 0, 0}, {1, 4, 3, 1, 0}, {1, 4, 3,
     ------------------------------------------------------------------------
     0, 0}, {1, 4, 2, 0, 0}, {1, 4, 1, 0, 0}, {1, 4, 0, 0, 0}, {1, 3, 3, 1,
     ------------------------------------------------------------------------
     0}, {1, 3, 3, 0, 0}, {1, 3, 2, 0, 0}, {1, 3, 1, 0, 0}, {1, 3, 0, 0, 0},
     ------------------------------------------------------------------------
     {1, 2, 1, 0, 0}, {1, 2, 0, 0, 0}, {1, 1, 0, 0, 0}, {1, 0, 0, 0, 0}, {0,
     ------------------------------------------------------------------------
     0, 0, 0, 0}, {-1, 0, 0, 0, 0}}

o2 : List

See also

Ways to use allHilbertSequences :

For the programmer

The object allHilbertSequences is a method function.