Proof step e-ed0a9060e2227d5c

basis_map A013610 → concludes about basis_map_A013610 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0. 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, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0. (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 dba95185bb0de830432688bc2ba3f23435ae89f20730d0fc34af1344d10859fc, 10,683 bytes (2,360 compressed); download JSON

Cited by

• n-18dc67fbac8ae269 (real_rooted)
• n-18dc67fbac8ae269 (one_signed_coefficients)
• n-18dc67fbac8ae269 (hadamard_kernel)
• n-18dc67fbac8ae269 (interlacing)