Proof step e-5d454ac027f458ad

basis_map A008277 → concludes about basis_map_A008277 of Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones. JSON

Theorem

Ray basis map theorem [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

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

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 c352e5a94ce415336d2941ebbb17cd7a30d53a46dc4bf7ee7a33bb18b2a78fd2, 7,759 bytes (1,528 compressed); download JSON

Cited by

• n-5a62d17a58e2a9f3 (one_signed_coefficients)
• n-5a62d17a58e2a9f3 (hadamard_kernel)
• n-5a62d17a58e2a9f3 (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