Proof step e-5535504a50c93560

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*12^j. 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

• Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*12^j. (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 2014e18f61bd70300c8c1c927f3113b20492d96fd77e35f84f8aeae1d4522433, 5,397 bytes (1,574 compressed); download JSON

Cited by

• n-101e6570094d0688 (real_rooted)
• n-101e6570094d0688 (one_signed_coefficients)
• n-101e6570094d0688 (hadamard_kernel)