Proof step e-1435140a6a62e1e4

basis_map A013610 → concludes about basis_map_A013610 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": "A013610",
  "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 30ed987a01e61ecb5044b21d75a41e9fa274717114749185b49e22cb3c5d6218, 14,259 bytes (2,677 compressed); download JSON

Cited by

• n-b1898a22ad30a15e (real_rooted)
• n-b1898a22ad30a15e (one_signed_coefficients)
• n-b1898a22ad30a15e (hadamard_kernel)
• n-b1898a22ad30a15e (interlacing)