Proof step e-c6b24692a36542e0

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows: T(n,k) is the number of k-matchings of the corona K'(n) of the complete graph K(n) and the complete graph K(1); in … 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) is the number of k-matchings of the corona K'(n) of the complete graph K(n) and the complete graph K(1); in o… (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 66833c8cc6f2cef3f1b15ce422baf486d1c471f246a73ec2ff335be9669b2a4f, 14,066 bytes (2,690 compressed); download JSON

Cited by

• n-6bbd968fe5cbbe11 (real_rooted)
• n-6bbd968fe5cbbe11 (one_signed_coefficients)
• n-6bbd968fe5cbbe11 (hadamard_kernel)
• n-6bbd968fe5cbbe11 (interlacing)