Proof step e-71d067081fff0c94

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of Triangle read by rows: T(n,k) = 2^floor(n/2)*binomial(n-1,k-1). 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 read by rows: T(n,k) = 2^floor(n/2)*binomial(n-1,k-1). (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 f616ef3350ccdd58e0df7cfe6421af44aa62e2aa50b04a2714e13359e12ef7c8, 5,394 bytes (1,581 compressed); download JSON

Cited by

• n-127551b414704b9e (real_rooted)
• n-127551b414704b9e (one_signed_coefficients)
• n-127551b414704b9e (hadamard_kernel)