Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A007318

Concludes

basis_map_A007318 of (10,1) Pascal triangle.

Premises

(10,1) Pascal triangle.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-d8d81e3e13cdd7d1 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Claims

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

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

Certificate

basis_map, SHA-256 3a61328f103ef4e9a28f16b15602b0883e30162a40f1425c4e50e50f52e7d3bb, 10,664 bytes (2,338 compressed); download

polytool replayed the certificate when the step was written.

Cited by