Proof step e-a6b5412d61e1c4e3

basis_map A013611 → concludes about basis_map_A013611 of Even-numbered rows of Pascal's triangle. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Even-numbered rows of Pascal's triangle. (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 645548f3b9fb60b23b9e00123df92de015307a3dfcc50d5763f9bb7b2bea53a3, 6,879 bytes (1,392 compressed); download JSON

Cited by

• n-0ca8dc857c80d449 (real_rooted)
• n-0ca8dc857c80d449 (one_signed_coefficients)
• n-0ca8dc857c80d449 (hadamard_kernel)