Proof step e-f19db33e28acf0c7

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1). 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) = binomial(n+k-1, 2*k-1). (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 37a7a141ede058926134559b2063bf68a33d6df271669cb80f2f5a491cd63a08, 13,345 bytes (2,522 compressed); download JSON

Cited by

• n-8fd7b2e367875124 (real_rooted)
• n-8fd7b2e367875124 (one_signed_coefficients)
• n-8fd7b2e367875124 (hadamard_kernel)
• n-8fd7b2e367875124 (interlacing)