Given a holonomic sequence $F(n)$, we characterize rational functions $r(n)$ so that $r(n)F(n)$ can be summable. We provide upper and lower bounds on the degree of the numerator of $r(k)$ and show the denominator of $r(n)$ can be read from annihilators of $F(k)$. This illustration provides the so-called rational reductions which can be used to generate new multi-sum equalities and congruences from known ones.
Dagstuhl Report 13082: Communication Complexity, Linear Optimization, and lower bounds for the nonnegative rank of matrices
Upper and lower bounds on $B_k^+$-sets
Lower bounds for designs in symmetric spaces
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