Real-rooted atlas

Proof step

Liu–Wang theorem

Theorem check of the sequence's own rule liu wang

Concludes
Elements in 3-Pascal triangle (by row).
Premises
none: a direct theorem check
Theorem
[LW07, Thm 2.1, Cor 2.4] ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-84b5e411b6df2e98 · JSON
Operation
Theorem check of the sequence's own rule
{
  "operation": "theorem_check",
  "theorem": "liu_wang"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": false,
      "value": "0"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 3,
  "kind": "weak",
  "orientation": "previous_interlaces_next"
}
Certificate
theorem_check, SHA-256 1ce0c7d7265d528657c0a0edb9ed1085e7476b87cba57454f95f8a094752abae, 3,661 bytes (1,170 compressed); download
polytool replayed the certificate when the step was written.
Cited by

References

  1. [LW07] Lily L. Liu and Yi Wang. A unified approach to polynomial sequences with only real zeros. Advances in Applied Mathematics, 38(4):542–560, May 2007. doi:10.1016/j.aam.2006.02.003