Proof step e-2f325d6b3b1beb16

basis_map A013609 → concludes about basis_map_A013609 of narayana JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• narayana (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 2, "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 4473652811530f97a237ac43bdb51f8ec4e9f4a6a9842e0a08efbfee61938035, 13,994 bytes (2,622 compressed); download JSON

Cited by

• n-f9bed40d8798da1b (real_rooted)
• n-f9bed40d8798da1b (one_signed_coefficients)
• n-f9bed40d8798da1b (hadamard_kernel)
• n-f9bed40d8798da1b (interlacing)