Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver affine, shift 0
- Concludes
- shift_x_plus_one of reversal of Triangle read by rows: T(n, k) = (k+1)*S2(n+1, k+1), for n >= k >= 0, and S2 = A048993 (Stirling2).
- Premises
- reversal of Triangle read by rows: T(n, k) = (k+1)*S2(n+1, k+1), for n >= k >= 0, and S2 = A048993 (Stirling2).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- reversal of Triangle read by rows: T(n, k) = (k+1)*S2(n+1, k+1), for n >= k >= 0, and S2 = A048993 (Stirling2).
- Theorem
- polytool ?
- Lean
- RealRooted
Polynomial.Splits.comp_of_degree_le_one - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-755c030e9032d39e· JSON- Operation
- Image under a real-rootedness preserver
{ "index_shift": 0, "operation": "preserver_image", "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}" } - Claims
{ "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "-1" } } }- Certificate
preserver_image, SHA-2561153d372ea7034e74d59443c5a5300da5e6284a09be0345a1ed2522a24d57cc6, 8,091 bytes (2,069 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-92978e16f285592e(real_rooted)n-92978e16f285592e(one_signed_coefficients)n-92978e16f285592e(hadamard_kernel)