Proof step

Liu–Wang theorem

Theorem check of the sequence's own rule liu wang

Concludes: Triangular array: the fusion of polynomial sequences P and Q given by p(n,x) = (x+2)^n and q(n,x) = (2*x+1)^n.
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-316a5efcd3478cb2 · 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 5a771c3af4b73722807ca6c07099727d7ad8c9f38160593f1d46a77424083e6c, 3,659 bytes (1,200 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