Proof step e-c5b76738fa9c73f6

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical let… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical lett… (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 4fc92632f438fc0407e11fdbf1cc48f3dc58c0a9e1e03baa16a1cf51516ed771, 6,855 bytes (1,389 compressed); download JSON

Cited by

• n-f6495b2c898daf02 (real_rooted)
• n-f6495b2c898daf02 (one_signed_coefficients)
• n-f6495b2c898daf02 (hadamard_kernel)