We investigate a class of truncated path algebras in which the Betti numbers of a simple module
satisfy a polynomial of arbitrarily large degree. We produce truncated path algebras where the
-th Betti number
of a simple module
is
for
and provide a result of the existence of algebras where
is a
polynomial of degree 4 or less with nonnegative integer coefficients. In particular, we
prove that this class of truncated path algebras produces Betti numbers
corresponding to any polynomial in a certain family.
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