Proof step e-23b30ca6e404c664

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of Array read by antidiagonals: number of antichains (or order ideals) in the poset 3*m*n or plane partitions with rows <= m, columns <= n and… 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

• Array read by antidiagonals: number of antichains (or order ideals) in the poset 3*m*n or plane partitions with rows <= m, columns <= n and… (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 b476e017e8c905bf7a58a9d5318807d974ab69f1eb5c37d9d5ab29996bb98652, 15,471 bytes (3,225 compressed); download JSON

Cited by

• n-7f59b8096b7b2635 (real_rooted)
• n-7f59b8096b7b2635 (one_signed_coefficients)
• n-7f59b8096b7b2635 (hadamard_kernel)