Proof step e-77b4dff64dd0f71c

basis_map A112227 → concludes about A scaled Hermite triangle. JSON

Theorem

Hermite-type basis map [MW08, Thm 2] polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A112227",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of A scaled Hermite triangle. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": {} }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 1e1492af5024be4114750c5d8ee039948d1ab798f3f45cc3f878537b36eac12a, 6,445 bytes (1,347 compressed); download JSON

Cited by

• n-0ce01d5a88917ba1 (real_rooted)

References

1. [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