Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver affine, shift 0
- Concludes
- shift_x_plus_one of basis_map_A013610 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0.
- Premises
- basis_map_A013610 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013610 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0.
- Theorem
- polytool ?
- Lean
- RealRooted
Polynomial.Splits.comp_of_degree_le_one - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-e061c0bd91278e18· 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": 0, "region": { "upper": { "closed": true, "value": "-1" } } }- Certificate
preserver_image, SHA-256984f7e050216982317e2057f2fc72df0aeeaf82659064a3e836bdea1415bfe73, 7,458 bytes (2,066 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-b1f50e3247c41c7c(real_rooted)n-b1f50e3247c41c7c(one_signed_coefficients)n-b1f50e3247c41c7c(hadamard_kernel)