Proof step e-2613ba1fbc2604f1

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 5ca2c1fafd081a33d52bc9d5d5e9c82c94513e644eab502d16297f59af4fd6a6, 7,469 bytes (1,633 compressed); download JSON

Cited by

• n-22e887254e1ffff8 (real_rooted)
• n-22e887254e1ffff8 (one_signed_coefficients)
• n-22e887254e1ffff8 (hadamard_kernel)