Abstract
By “squeezing the combinatorics out” of Kathy O’Hara’s magnificent combinatorial proof of the unimodality of the Gaussian polynomials [n k] we give an extremely short and elementary proof of this unimodality for k < any fixed integer, and a fairly short, semi-combinatorial proof for general k. Combined with Macdonald’s paper in this volume the present paper implies an entirely elementary algebraic proof of the unimodality of the Gaussian polynomials.
Supported in part by the NSF grant DMS 8800663
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Zeilberger, D. (1989). A One-Line High School Algebra Proof of the Unimodality of the Gaussian Polynomials [ nk ] for k < 20. In: Stanton, D. (eds) q-Series and Partitions. The IMA Volumes in Mathematics and Its Applications, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0637-5_6
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DOI: https://doi.org/10.1007/978-1-4684-0637-5_6
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