Proof step e-15636530e2574f08

preserver_image affine, shift 0 → concludes about shift_x_plus_one 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 antidiagonals… JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): Polynomial.Splits.comp_of_degree_le_one

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

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": "-1" } } }
• { "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: preserver_image, SHA-256 27dd95e0d3ee68ca2377ad94b64a40beb3c6284d7254f84ecd2ef87ced932679, 22,064 bytes (5,258 compressed); download JSON

Cited by

• n-40ba0d1f2a40a97e (interlacing)
• n-40ba0d1f2a40a97e (real_rooted)
• n-40ba0d1f2a40a97e (one_signed_coefficients)
• n-40ba0d1f2a40a97e (hadamard_kernel)