Proof step e-f21031c0731e2731

basis_map A013611 → concludes about basis_map_A013611 of Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k). (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 040def2249af0fb0a5112e65924da70dd068e7e2be0655291175f55ea836ef6c, 7,409 bytes (1,616 compressed); download JSON

Cited by

• n-ce701caf7dd0b8e7 (real_rooted)
• n-ce701caf7dd0b8e7 (one_signed_coefficients)
• n-ce701caf7dd0b8e7 (hadamard_kernel)