Proof step e-f9ff31509ec6911f

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 ff837b030a803472f0ea847541bcd846155c221aedc4acf8e293716fd073a43a, 10,724 bytes (2,409 compressed); download JSON

Cited by

• n-04616b0b8f6da9ca (real_rooted)
• n-04616b0b8f6da9ca (one_signed_coefficients)
• n-04616b0b8f6da9ca (hadamard_kernel)
• n-04616b0b8f6da9ca (interlacing)