Lattice Paths and Positive Trigonometric Sums
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A trigonometric polynomial generalization to the positivity of an alternating sum of binomial coefficients is given. The proof uses lattice paths, and identifies the trigonometric sum as a polynomial with positive integer coefficients. Some special cases of the q -analogue conjectured by Bressoud are established, and new conjectures are given.
- Lattice Paths and Positive Trigonometric Sums
Volume 15, Issue 1 , pp 69-81
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- Key words. Lattice paths, Binomial coefficients, Quadrature, Positivity. AMS Classification. Primary: 42A32; Secondary: 05C38.