Proof step e-258aa4ea5bc7ae92

basis_map A013610 → concludes about basis_map_A013610 of Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 2, "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 a92952617308b3ca98a1a75b4cd3ac82e490a9074c9d6a0c9b85f06919d73116, 13,345 bytes (2,523 compressed); download JSON

Cited by

• n-b362ab32ef269db1 (real_rooted)
• n-b362ab32ef269db1 (one_signed_coefficients)
• n-b362ab32ef269db1 (hadamard_kernel)
• n-b362ab32ef269db1 (interlacing)