Proof step e-88e5d38a889ee296

basis_map A013610 → concludes about basis_map_A013610 of Triangle read by rows: T(n,k) = binomial(2n+1, 2k+1). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) = binomial(2n+1, 2k+1). (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 c1325892852917c42bd5fabdbaff3fb56e0741f1f017468b5e54b2a70980d0c0, 13,634 bytes (2,585 compressed); download JSON

Cited by

• n-966c4f25f43e716e (real_rooted)
• n-966c4f25f43e716e (one_signed_coefficients)
• n-966c4f25f43e716e (hadamard_kernel)
• n-966c4f25f43e716e (interlacing)