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Gaps between consecutive divisors of factorials

Daniel Berend, J. E. Harmse (1993)

Annales de l'institut Fourier

The set of all divisors of n ! , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest n ! and obtain a lower bound on their distance.

Generalizations of Milne’s U ( n + 1 ) q -Chu-Vandermonde summation

Jian-Ping Fang (2016)

Czechoslovak Mathematical Journal

We derive two identities for multiple basic hyper-geometric series associated with the unitary U ( n + 1 ) group. In order to get the two identities, we first present two known q -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two U ( n + 1 ) q -Chu-Vandermonde summations established by Milne, we arrive at our...

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