Proof step

Liu–Wang theorem

Theorem check of the sequence's own rule liu wang

Concludes: Triangle T(n, k) = 2*binomial(n, k) with T(0, 0) = 1, 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-8527a7cb3f2fcf05 · 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 6c9b20fb0c452fad5d3703209fb1b9da74331fe190ce5dc527972a85e900b159, 3,647 bytes (1,165 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