Proof step e-31057cc4a5bc6e44

basis_map A013609 → concludes about basis_map_A013609 of Triangular array T read by rows: T(n,0) = T(n,n) = 1 for all n >= 0, T(n,k) = T(n-1,k-1) + T(n-1,k) for odd n and 1< = k <= n-1, T(n,k) = … JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangular array T read by rows: T(n,0) = T(n,n) = 1 for all n >= 0, T(n,k) = T(n-1,k-1) + T(n-1,k) for odd n and 1< = k <= n-1, T(n,k) = T… (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 a35575c6b4e4892ca70bc89d5a9e7dee7377cbbc2bd04b640e0496465a69449d, 6,927 bytes (1,409 compressed); download JSON

Cited by

• n-8b4c5b34b9871b90 (real_rooted)
• n-8b4c5b34b9871b90 (one_signed_coefficients)
• n-8b4c5b34b9871b90 (hadamard_kernel)