Proof step e-017120e86183432c

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

• Table a(d,m) of number of points of L1 norm m in cubic lattice Z^d, read by antidiagonals (d >= 1, m >= 0). (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 c2d5e2cc292636302e16b5cdf242ba303f3345d18df61e009bc18c9111b9f982, 14,011 bytes (2,698 compressed); download JSON

Cited by

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