Proof step e-8cd26e1d1ff01e6d

basis_map A013610 → concludes about basis_map_A013610 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": "A013610",
  "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 90aa9c99d21a3ab8ade916f40bf23afc5047b8cd2623c6916acdf0e192969a4d, 13,451 bytes (2,555 compressed); download JSON

Cited by

• n-f5286435ed391b4f (real_rooted)
• n-f5286435ed391b4f (one_signed_coefficients)
• n-f5286435ed391b4f (hadamard_kernel)
• n-f5286435ed391b4f (interlacing)