Proof step

Ray basis map theorem

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

Concludes

Premises

Triangle read by rows, T(n,k) = (n+1)*binomial(n-1,k-1).
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-f9832e6a5c7b3771 · 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 e4ae65f9a24b77e8f6bd206ca406a0d677bf2ad2df6688b38a4e44c80aacfaa1, 15,763 bytes (2,991 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