Proof step e-46c4bb14ef9f43a7

basis_map A007318 → concludes about basis_map_A007318 of Square array A(n,r), the number of neighbors at a sharp Manhattan distance r in a finite n-hypercube lattice, read by upwards antidiagonal… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Square array A(n,r), the number of neighbors at a sharp Manhattan distance r in a finite n-hypercube lattice, read by upwards antidiagonals… (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": 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 b696019720408d984e3a776b17afca59eb1217e52450353897f39f0cbeca5db0, 14,305 bytes (2,776 compressed); download JSON

Cited by

• n-9ac33c0e4aa39b7d (interlacing)
• n-9ac33c0e4aa39b7d (real_rooted)
• n-9ac33c0e4aa39b7d (one_signed_coefficients)
• n-9ac33c0e4aa39b7d (hadamard_kernel)