Proof step e-e6f59c3f9755ffec

basis_map A013611 → concludes about basis_map_A013611 of narayana JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "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 b69179c2c52f252ffd8c1f253735fc6f4f989d2d3de9b000d244231b0284c29c, 13,998 bytes (2,625 compressed); download JSON

Cited by

• n-3af50523900b3357 (real_rooted)
• n-3af50523900b3357 (one_signed_coefficients)
• n-3af50523900b3357 (hadamard_kernel)
• n-3af50523900b3357 (interlacing)