Proof step e-7f59bcf02d573532

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 e7ffddf2df79febc51e2459f661b03694a7777649ee38ab4ec0e8fea10b943cb, 14,001 bytes (2,634 compressed); download JSON

Cited by

• n-60c7f085d1907563 (real_rooted)
• n-60c7f085d1907563 (one_signed_coefficients)
• n-60c7f085d1907563 (hadamard_kernel)
• n-60c7f085d1907563 (interlacing)