Proof step e-d700e7dd8b41ed69

basis_map A007318 → concludes about shift_x_plus_one 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": "A007318",
  "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 1d9602f937ab7f407a61a87cc1292e35c4d2f3eb3d3a84f83aec6cd7b7394098, 10,545 bytes (2,309 compressed); download JSON

Cited by

• n-8159f24e9c9fb552 (one_signed_coefficients)
• n-8159f24e9c9fb552 (hadamard_kernel)
• n-8159f24e9c9fb552 (real_rooted)
• n-8159f24e9c9fb552 (interlacing)