In 1974, the author proved that the codimension of the ideal
generated in the group algebra
over a field
of characteristic 0 by generic Laurent
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In 1974, the author proved that the codimension of the ideal
generated in the group algebra
over a field
of characteristic 0 by generic Laurent polynomials having the same Newton polytope
is equal to
. Assuming that Newtons polytope is
simplicial and
super-convenient (that is, containing some neighborhood of the origin), the author strengthens the 1974 result by explicitly specifying the set
of monomials of cardinality
, whose equivalence classes form a basis of the quotient algebra
. The set
is constructed inductively from any shelling
of the polytope
. Using the
structure, we prove that the associated graded
-algebra
constructed from the Arnold–Newton filtration of
-algebra
has the Cohen–Macaulay property. This proof is a generalization of B. Kind and P. Kleinschmitt’s 1979 proof that Stanley–Reisner rings of simplicial complexes admitting shelling are Cohen–Macaulay. Finally, we prove that for generic Laurent polynomials
with the same Newton polytope
, the set
defines a monomial basis of the quotient algebra
.
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