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$q$-rious unimodality

S. Ole Warnaar, Wadim Zudilin

Abstract

We generalise our still-wide-open $q$-rious positivity conjecture from 2011 to a $q$-rious unimodality conjecture.

$q$-rious unimodality

Abstract

We generalise our still-wide-open -rious positivity conjecture from 2011 to a -rious unimodality conjecture.

Paper Structure

This paper contains 1 section, 5 theorems, 32 equations.

Table of Contents

  1. Acknowledgement

Key Result

Lemma 2

If $(\boldsymbol{a},\boldsymbol{b})$ satisfies Landau II then Landau I holds and $(\boldsymbol{a},\boldsymbol{b})$ is balanced.

Theorems & Definitions (11)

  • Conjecture 1: $q$-rious positivity
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 4: WZ11
  • Conjecture 5: $q$-rious unimodality
  • Lemma 6
  • proof
  • Remark
  • ...and 1 more