Proof step e-0f31cc897fc45a50

basis_map A013609 → concludes about Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*10^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j)*5^j. (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 64ee37337478dfef978bd9e3f787e307252d9489551db15a30d6c2629c95b2ad, 6,859 bytes (1,392 compressed); download JSON

Cited by

• n-e1d1088f7d1ff894 (one_signed_coefficients)
• n-e1d1088f7d1ff894 (hadamard_kernel)
• n-e1d1088f7d1ff894 (real_rooted)