Proof step e-d718d4a3c4d020a8

basis_map A013610 → concludes about basis_map_A013610 of Triangle of Bessel numbers read by rows: T(n,k) is the number of k-matchings of the complete graph K(n). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle of Bessel numbers read by rows: T(n,k) is the number of k-matchings of the complete graph K(n). (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 f4206575d33b2883598110be068bfb349210a09cc3cc19af3a4bfd2ef5eee5e0, 10,545 bytes (2,315 compressed); download JSON

Cited by

• n-e5924eef99dd90a5 (real_rooted)
• n-e5924eef99dd90a5 (one_signed_coefficients)
• n-e5924eef99dd90a5 (hadamard_kernel)
• n-e5924eef99dd90a5 (interlacing)