Proof step e-1a0f394398e61cd4

basis_map A013609 → concludes about basis_map_A013609 of Triangle T(n,k) read by rows: number of size-k antisymmetric subsets of {1,2,...,n}. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle T(n,k) read by rows: number of size-k antisymmetric subsets of {1,2,...,n}. (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: basis_map, SHA-256 4fffb1a0b101b1a4e68e866670be0c6f85820077acdcc5de8c684bb6d43dff45, 6,885 bytes (1,393 compressed); download JSON

Cited by

• n-2114ace3c07775a2 (real_rooted)
• n-2114ace3c07775a2 (one_signed_coefficients)
• n-2114ace3c07775a2 (hadamard_kernel)