Proof step e-3261655b8c5a1522

gamma_polynomial scale 1, shift 1 → concludes about Triangular array of Motzkin polynomial coefficients. JSON

Theorem

Gamma criterion RealRooted IsGammaExpansion.isRealRooted_and_hasRootsNonpos_iff ?

Operation

Gamma polynomial of a palindromic parent

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

Premises

• narayana (sequence)
  uses: Every row P_n, n >= 1, 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 997e2b58036c2d8adf6bbcfbf9f73f1e57ca7f7cf6a2e698ea3102fc8dc4da70, 10,523 bytes (2,326 compressed); download JSON

Cited by

• n-169bd483754ab390 (real_rooted)
• n-169bd483754ab390 (one_signed_coefficients)
• n-169bd483754ab390 (hadamard_kernel)