Proof step e-50a19be1a64262f5

basis_map A013611 → concludes about basis_map_A013611 of Even row Pascal-square read by antidiagonals. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Even row Pascal-square read by antidiagonals. (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 e9f9d97b244c5da94bb8e8fd8667380c8fa96e90dc7daab7f53bd2207adc11bf, 13,624 bytes (2,602 compressed); download JSON

Cited by

• n-45aade2d3fba368c (real_rooted)
• n-45aade2d3fba368c (one_signed_coefficients)
• n-45aade2d3fba368c (hadamard_kernel)
• n-45aade2d3fba368c (interlacing)