Proof step e-d797656a7302c65e

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: T(n,k) is the number of lattice paths from (0,0) to (n,n) using steps E=(1,0), N=(0,1) and D=(1,1) (i.e., bilateral… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) is the number of lattice paths from (0,0) to (n,n) using steps E=(1,0), N=(0,1) and D=(1,1) (i.e., bilateral … (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": { "upper": { "closed": true, "value": "0" } } }
• { "claim": "interlacing", "from_index": 2, "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 84396de183cd124102c9964da153ce4409af8c92288bcfddb8562fd8aad22310, 14,009 bytes (2,637 compressed); download JSON

Cited by

• n-6373ae06480cbab5 (real_rooted)
• n-6373ae06480cbab5 (one_signed_coefficients)
• n-6373ae06480cbab5 (hadamard_kernel)
• n-6373ae06480cbab5 (interlacing)