Proof step e-c271a57d901f1e05

basis_map A013611 → concludes about basis_map_A013611 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": "A013611",
  "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 16a6a227cebe7541a94c0ddd8ab11eb328ee7b819708f83f79c23db3d83f62f5, 7,414 bytes (1,620 compressed); download JSON

Cited by

• n-1a01d480c8d600c3 (real_rooted)
• n-1a01d480c8d600c3 (one_signed_coefficients)
• n-1a01d480c8d600c3 (hadamard_kernel)