Proof step e-037c1a08736a9fd9

gamma_polynomial scale 1, shift 0 → concludes about Triangle of Bessel numbers read by rows: T(n,k) is the number of k-matchings of the complete graph K(n). 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) is the number of k-matchings of the corona K'(n) of the complete graph K(n) and the complete graph K(1); in o… (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 ce49da729642bb1c9d992b199d1c5e4531c3a8efd3c11dbf180327cea22f86e7, 10,802 bytes (2,516 compressed); download JSON

Cited by

• n-97b51734d39ede6c (real_rooted)
• n-97b51734d39ede6c (one_signed_coefficients)
• n-97b51734d39ede6c (hadamard_kernel)