In the work The Friedman–Joichi–Stanton Monotonicity Conjecture at Primes, George Andrews gave a proof of the fact (first mentioned by Jim Propp a while ago) that the q-binomial coefficient View the MathML source divided by the q-integer [n]q is a polynomial in q, as long as n and k are relatively prime (see [G.E. Andrews, The Friedman–Joichi–Stanton Monotonicity Conjecture at Primes, in: DIMACS Ser., Amer. Math. Soc., in press, Theorem 2]). In this note we provide a proof that permits to generalize Theorem 2 in the case in which n and k are not relatively prime, and further, to extend Theorem 2 to the q-multinomial coefficient.
Brunetti, S., DEL LUNGO, A. (2004). On the polynomial 1/[n]q [kn] q. ADVANCES IN APPLIED MATHEMATICS, 33(3), 487-491 [10.1016/j.aam.2004.03.001].
On the polynomial 1/[n]q [kn] q
BRUNETTI S.;
2004-01-01
Abstract
In the work The Friedman–Joichi–Stanton Monotonicity Conjecture at Primes, George Andrews gave a proof of the fact (first mentioned by Jim Propp a while ago) that the q-binomial coefficient View the MathML source divided by the q-integer [n]q is a polynomial in q, as long as n and k are relatively prime (see [G.E. Andrews, The Friedman–Joichi–Stanton Monotonicity Conjecture at Primes, in: DIMACS Ser., Amer. Math. Soc., in press, Theorem 2]). In this note we provide a proof that permits to generalize Theorem 2 in the case in which n and k are not relatively prime, and further, to extend Theorem 2 to the q-multinomial coefficient.
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https://hdl.handle.net/11365/25423
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