Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A007318

Concludes

Premises

veronese_section_2_1 of Triangle of coefficients in expansion of (1+3*x)^n.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-77e1fbc8cee25830 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

{
  "claim": "interlacing",
  "from_index": 2,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 5bbeaa8d838808b4b0977a2fdfeaec83b977d79ec30c13509fea2a90d3c7bb43, 15,010 bytes (3,008 compressed); download

polytool replayed the certificate when the step was written.

Cited by