Proof step e-32ae8a16e295b946

basis_map A013609 → concludes about basis_map_A013609 of Matrix product of unsigned Lah-triangle |A008297(n,k)| and unsigned Stirling1-triangle |A008275(n,k)|. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Matrix product of unsigned Lah-triangle |A008297(n,k)| and unsigned Stirling1-triangle |A008275(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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 13a28446a7f42bdaefef2acca9341c11b060e06c3907cfb9ac0c4b7d02f4dd23, 13,465 bytes (2,549 compressed); download JSON

Cited by

• n-9ac71617f56e595e (real_rooted)
• n-9ac71617f56e595e (one_signed_coefficients)
• n-9ac71617f56e595e (hadamard_kernel)
• n-9ac71617f56e595e (interlacing)