Proof step

Ray basis map theorem

Image under a basis map u^k -> P_k A008277

Concludes

Premises

basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*3^j.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-8092959d5758c207 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A008277",
  "operation": "basis_map"
}

Claims

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

Certificate

basis_map, SHA-256 555771634fd276e2da5aa2af746f2ef6487462f426ca47e3a0f796498340f5de, 7,527 bytes (1,504 compressed); download

polytool replayed the certificate when the step was written.

Cited by

References

[MW08] Shi-Mei Ma and Yi Wang. q-Eulerian polynomials and polynomials with only real zeros. The Electronic Journal of Combinatorics, 15(1):Research Paper 17, January 2008. doi:10.37236/741