Proof step e-1e993b9b3c7faf34

theorem_check liu_wang_derivative_lag → concludes about 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; A(n,r) = Sum_{k=0.… JSON

Theorem

Liu–Wang theorem with a lag row [LW07, Thm 2.1] RealRooted ?

Lean (RealRooted): route sign RealRooted.threeTerm_interlaces_of_nonnegCoeffs, RealRooted.LiuWang.strictInterl_nonpos_lag_sequence

Operation

Theorem check of the node's own rule

{
  "operation": "theorem_check",
  "theorem": "liu_wang_derivative_lag"
}

Premises

None: this step is a direct theorem check.

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": false, "value": "0" } } }
• { "claim": "interlacing", "from_index": 2, "kind": "strict", "orientation": "previous_interlaces_next" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: theorem_check, SHA-256 197236277da44bbb143fa241a387f3ae020be3389cc3d164bf7990c3b0042cf6, 5,203 bytes (1,531 compressed); download JSON

Cited by

• n-a1540a6d32c29f8f (real_rooted)
• n-a1540a6d32c29f8f (one_signed_coefficients)
• n-a1540a6d32c29f8f (hadamard_kernel)
• n-a1540a6d32c29f8f (interlacing)

References

1. [LW07] Lily L. Liu and Yi Wang. A unified approach to polynomial sequences with only real zeros. Advances in Applied Mathematics, 38(4):542–560, May 2007. doi:10.1016/j.aam.2006.02.003