Title

On Bergeron's positivity problem for q -binomial coefficients

Document Type

Article

Publication Date

4-27-2018

Abstract

F. Bergeron recently asked the intriguing question whether ((b+c)/b)q-((a+d)/d)q has nonnegative coefficients as a polynomial in q, whenever a, b, c, dare positive integers, a is the smallest, and ad=bc. We conjecture that, in fact, this polynomial is also always unimodal, and combinatorially show our conjecture for a≤3 and any b, c≥4. The main ingredient will be a novel (and rather technical) applicationof Zeilberger’s KOH theorem.

Publisher's Statement

© The author. Released under the CC BY-ND license (International 4.0). Publisher’s version of record: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i2p17

Publication Title

The Electronic Journal of Combinatorics

Creative Commons License

Creative Commons Attribution-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-No Derivative Works 4.0 License.

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