Proof step e-45b4054949a52789

basis_map A013610 → concludes about basis_map_A013610 of Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); .... JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); .... (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 af9935ec167ce214f1a231105f7dd54ed550b49640310d84faea5a1d0c0fa2dd, 10,157 bytes (2,282 compressed); download JSON

Cited by

• n-70594f2875298da0 (real_rooted)
• n-70594f2875298da0 (one_signed_coefficients)
• n-70594f2875298da0 (hadamard_kernel)
• n-70594f2875298da0 (interlacing)