Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013610

Concludes

Premises

Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-30d3ba79234af592 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

{
  "claim": "interlacing",
  "from_index": 2,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 f90444c3412d7e2c52fe8b4763140fcd4b0336c991eb6359e3b7ac16d63b7a94, 13,480 bytes (2,559 compressed); download

polytool replayed the certificate when the step was written.

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