Proof step e-afc618911e5721d2

basis_map A013610 → concludes about basis_map_A013610 of Triangle T(n,k) giving number of degree-2n permutations which decompose into exactly k cycles of even length, k=0..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 T(n,k) giving number of degree-2n permutations which decompose into exactly k cycles of even length, k=0..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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 df354c2ac126062923a0be95874fe1da678a644be8265dd3b452b8ac24d21151, 7,469 bytes (1,633 compressed); download JSON

Cited by

• n-77311ba2b23da2eb (real_rooted)
• n-77311ba2b23da2eb (one_signed_coefficients)
• n-77311ba2b23da2eb (hadamard_kernel)