#11411: some q binomial coefficients should be zero
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Reporter: chapoton | Owner: sage-combinat
Type: defect | Status: needs_review
Priority: minor | Milestone:
Component: combinatorics | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Description changed by chapoton:
Old description:
> I have found the following behaviour:
>
> {{{
> sage: import sage.combinat.q_analogues as qa
> sage: qa.q_binomial(2,-1)
> 1/(q^2 + q + 1)
> sage: binomial(2,-1)
> 0
> sage: qa.q_binomial(2,3)
> 1/(q^2 + q + 1)
> sage: binomial(2,3)
> 0
> }}}
> I think these q-binomials should rather be zero. The q-binomial is based
> on the q-factorial, where one finds the following behaviour
>
> {{{
> sage: [qa.q_factorial(-i) for i in range(6)]
> [1, 1, 1, 1, 1, 1]
> }}}
>
> This seems to be rather wrong, as the factorial itself is infinite for
> negative integers.
New description:
I have found the following behaviour:
{{{
sage: import sage.combinat.q_analogues as qa
sage: qa.q_binomial(2,-1)
1/(q^2 + q + 1)
sage: binomial(2,-1)
0
sage: qa.q_binomial(2,3)
1/(q^2 + q + 1)
sage: binomial(2,3)
0
}}}
I think these q-binomials should rather be zero. The q-binomial is based
on the q-factorial, where one finds the following behaviour
{{{
sage: [qa.q_factorial(-i) for i in range(6)]
[1, 1, 1, 1, 1, 1]
}}}
This seems to be rather wrong, as the factorial itself is infinite for
negative integers.
The patch restricts the q-factorial to nonnegative arguments and defines
q-binomials outside of the correct range to be zero.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11411#comment:2>
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