Proof step e-fe4cc1f9dd1d3096

basis_map A013610 → concludes about basis_map_A013610 of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. sh… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shi… (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": 1, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 20cbb3c61fd5b1d7f37d6fca035b9e99f5969bf90546867ae33c0d96b921f639, 6,862 bytes (1,395 compressed); download JSON

Cited by

• n-1cfea80692e421ba (real_rooted)
• n-1cfea80692e421ba (one_signed_coefficients)
• n-1cfea80692e421ba (hadamard_kernel)