Proof step e-d3f9f2e05c32db01

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 0eaea89eb17bd731740917c7b8e5cbb4bf4e3f0d0d50634dd0b5ecb44e2dd563, 7,414 bytes (1,622 compressed); download JSON

Cited by

• n-20bccc4c38847de1 (real_rooted)
• n-20bccc4c38847de1 (one_signed_coefficients)
• n-20bccc4c38847de1 (hadamard_kernel)