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

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:

  • allHilbertSequences(Ring)

For the programmer

The object allHilbertSequences is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/ExteriorIdeals.m2:535:0.