Proof step e-0b9b63070f7f0adc

basis_map A007318 → concludes about shift_x_plus_one 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": "A007318",
  "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 7bc26e04c1fe531ed76d37e546cd4a63ee4a882bb0711ddc76d24a727fa44cb8, 6,885 bytes (1,392 compressed); download JSON

Cited by

• n-4e8690098ee9d7b4 (one_signed_coefficients)
• n-4e8690098ee9d7b4 (hadamard_kernel)
• n-4e8690098ee9d7b4 (real_rooted)