Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- reversal of Triangle read by rows, coefficients of the generalized Eulerian polynomials A_{n, 3}(x) in descending order.
- Premises
- Triangle read by rows, coefficients of the generalized Eulerian polynomials A_{n, 3}(x) in descending order.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows, coefficients of the generalized Eulerian polynomials A_{n, 3}(x) in descending order.
- Theorem
- polytool ?
- Lean
- RealRooted
route
reversedRealRooted.X_pow_mul_reverse_eq_zero_or_splits,RealRooted.reflect_eq_zero_or_splits - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-ce3f869810cfd5d2· JSON- Operation
- Image under a real-rootedness preserver
{ "index_shift": 0, "operation": "preserver_image", "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":1,\"first_degree\":0,\"step\":1}}" } - Claims
{ "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
preserver_image, SHA-2562e557a6e758e76b9420c94d3f65a957d0f60af34a007d97f837b49baa1d93a74, 10,699 bytes (2,715 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-89455cdf5080c940(real_rooted)n-89455cdf5080c940(one_signed_coefficients)n-89455cdf5080c940(hadamard_kernel)