Proof step e-021513687e7cc411

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 449c95f9807fb9575d5935043b7019894abb83e818bbb991da6d18a7ece74961, 13,465 bytes (2,545 compressed); download JSON

Cited by

• n-843f07b55ed17e8a (real_rooted)
• n-843f07b55ed17e8a (one_signed_coefficients)
• n-843f07b55ed17e8a (hadamard_kernel)
• n-843f07b55ed17e8a (interlacing)