Proof step e-ac961eccb8b6d01b

basis_map A007318 → concludes about shift_x_plus_one of Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318). (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 6a162f8b526499cf96cac01bcfa0fe73b33da79d10cdebfc99d7ce35918f5106, 10,724 bytes (2,406 compressed); download JSON

Cited by

• n-6e06ff1c41cd6465 (one_signed_coefficients)
• n-6e06ff1c41cd6465 (hadamard_kernel)
• n-6e06ff1c41cd6465 (real_rooted)
• n-6e06ff1c41cd6465 (interlacing)