Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013609

Concludes
basis_map_A013609 of 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.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-9c3505dcd599244b · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A013609",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
basis_map, SHA-256 e40f555bdc1f9e8238d849b28aaef8d945b0a991d0b59447afd7a0bfc23c1e28, 10,342 bytes (2,319 compressed); download
polytool replayed the certificate when the step was written.
Cited by