Proof step e-d1c49253f9d90c32

basis_map A013611 → concludes about basis_map_A013611 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": "A013611",
  "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 c93075084a7ec83b76f17c1b0e018948187b67261115213dc094fc5cf7d68eca, 6,885 bytes (1,396 compressed); download JSON

Cited by

• n-8a70fbd3ff1954d6 (one_signed_coefficients)
• n-8a70fbd3ff1954d6 (hadamard_kernel)
• n-8a70fbd3ff1954d6 (real_rooted)