Proof step e-8877bf17db51e7c6

basis_map A013610 → concludes about basis_map_A013610 of basis-map coefficients of Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)}… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Triangle read by rows: BellMatrix(Product_{p in P(n)} p), where P(n) = {k : k mod m = 1 and 1 <= k <= m*(n + 1)} … (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 50ac708caa51a37bde202fb6de0a630493cc1fed2e07527738610f7eab659b63, 7,414 bytes (1,621 compressed); download JSON

Cited by

• n-b0592fccca597966 (real_rooted)
• n-b0592fccca597966 (one_signed_coefficients)
• n-b0592fccca597966 (hadamard_kernel)