Proof step e-b82c219011a0bccd

basis_map A013609 → concludes about basis_map_A013609 of T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows. (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 99e6337970fdfb45ced8f1cbaccdda6c6772d1f7b8b7aec601c0238543cd9218, 13,673 bytes (2,561 compressed); download JSON

Cited by

• n-dfe248045567f938 (real_rooted)
• n-dfe248045567f938 (one_signed_coefficients)
• n-dfe248045567f938 (hadamard_kernel)
• n-dfe248045567f938 (interlacing)