Proof step e-c5fd3da4c5a13f73

basis_map A007318 → concludes about basis_map_A007318 of Pascal-(1,7,1) array. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Pascal-(1,7,1) array. (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 927aca87ce4807aad9684500b4dfc3de0b03f77e1f3baeba350224060667064d, 14,011 bytes (2,699 compressed); download JSON

Cited by

• n-9f4396728047edfb (real_rooted)
• n-9f4396728047edfb (one_signed_coefficients)
• n-9f4396728047edfb (hadamard_kernel)
• n-9f4396728047edfb (interlacing)