Proof step e-cd3fa89de2aead53

basis_map A007318 → concludes about shift_x_plus_one of Triangle read by rows: T(n,k) = binomial(k,n-k). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) = binomial(k,n-k). (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 76cb2efb0bc62db89c8196124f74a985c332791a1750029b0ec13a502177ce37, 11,582 bytes (2,147 compressed); download JSON

Cited by

• n-51a2369b25b8e3ba (one_signed_coefficients)
• n-51a2369b25b8e3ba (hadamard_kernel)
• n-51a2369b25b8e3ba (real_rooted)