Proof step e-250eeed7ad07d148

gamma_polynomial scale 1, shift 0 → concludes about 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 (0 <= k <= floor(n/2… JSON

Theorem

Gamma criterion RealRooted IsGammaExpansion.isRealRooted_and_hasRootsNonpos_iff ?

Operation

Gamma polynomial of a palindromic parent

{
  "index_shift": 0,
  "operation": "gamma_polynomial",
  "scale": "1"
}

Premises

• Pascal-(1,2,1) array read by antidiagonals. (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: gamma_polynomial, SHA-256 c510169b4a05033d80a373255159ffad183c5fbaac396c59b2a69d812e060102, 10,504 bytes (2,405 compressed); download JSON

Cited by

• n-e3d901814302c059 (real_rooted)
• n-e3d901814302c059 (one_signed_coefficients)
• n-e3d901814302c059 (hadamard_kernel)