Proof step

Liu–Wang theorem

Theorem check of the sequence's own rule liu wang

Concludes: row_factor parent of Triangle read by rows: T(n,k), for k=-n..n-1, is the scaled (by 2^n n!) probability that the sum of n uniform [-1, 1] variables is between…
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-934a027fe06e0c1b · 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": 1,
  "kind": "weak",
  "orientation": "previous_interlaces_next"
}

Certificate

theorem_check, SHA-256 b90067f349feca015e8fe396b6b5cd15f1956cd7817efb8b78736e4d63978fd5, 3,288 bytes (1,113 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