Lattice Paths and Positive Trigonometric Sums
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- Ismail, M., Kim, D. & Stanton, D. Constr. Approx. (1999) 15: 69. doi:10.1007/s003659900097
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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.