Proof step e-099e290d18ba9894

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: T(n,k) is the number of ways to tile a 3 X n rectangle with k pieces of 2 X 2 tiles and 3n-4k pieces of 1 X 1 tiles… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) is the number of ways to tile a 3 X n rectangle with k pieces of 2 X 2 tiles and 3n-4k pieces of 1 X 1 tiles … (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 7121c158fc9921c22a8c1fc7b0cc157a58a335694a82c999637c58389bc128e5, 10,696 bytes (2,409 compressed); download JSON

Cited by

• n-af7a69a897cce4e9 (real_rooted)
• n-af7a69a897cce4e9 (one_signed_coefficients)
• n-af7a69a897cce4e9 (hadamard_kernel)
• n-af7a69a897cce4e9 (interlacing)