Proof step

Liu–Wang theorem

Theorem check of the sequence's own rule liu wang

Concludes: Triangular matrix arising in enumeration of catafusenes, read by rows.
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-1bf12aada4464177 · 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": 2,
  "kind": "weak",
  "orientation": "previous_interlaces_next"
}

Certificate

theorem_check, SHA-256 cf8fed79012c5a94096262602364a882d5226c88fda4754c3b7b1edadb55dc72, 3,653 bytes (1,184 compressed); download

polytool replayed the certificate when the step was written.

Cited by

References

[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