Proof step e-aca51a80a394c762

basis_map A013609 → concludes about basis_map_A013609 of Triangle T(n, k) of numbers of square lattice walks that start and end at origin after 2*n steps and contain exactly k steps to the east, … JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle T(n, k) of numbers of square lattice walks that start and end at origin after 2*n steps and contain exactly k steps to the east, p… (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 bd76b24e001f67bca66e4ffd1a49bedaf6b42480131fb7f078ab33fac08e3ff4, 14,255 bytes (2,673 compressed); download JSON

Cited by

• n-db27c4ac13806435 (real_rooted)
• n-db27c4ac13806435 (one_signed_coefficients)
• n-db27c4ac13806435 (hadamard_kernel)
• n-db27c4ac13806435 (interlacing)