Proof step e-125a67b606fd2347

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows: T(n,k) number of tilings of a 2n X 3 grid by dominoes, 2k of which are in a vertical position (0<=k<=n). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle read by rows: T(n,k) number of tilings of a 2n X 3 grid by dominoes, 2k of which are in a vertical position (0<=k<=n). (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 09327501c6d30bcf8d2064907257dec3cda2c43593f48e82db973ffcc0ab50d0, 13,449 bytes (2,553 compressed); download JSON

Cited by

• n-d5dd236ae5fa65ba (real_rooted)
• n-d5dd236ae5fa65ba (one_signed_coefficients)
• n-d5dd236ae5fa65ba (hadamard_kernel)
• n-d5dd236ae5fa65ba (interlacing)