Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- Triangle T(n, k) = coefficients of p(x, n) where p(x,n) = (x+1)*p(x, n-1) + n*(n-1)*x*p(x, n-2), read by rows.
- Premises
- Triangle T(n, k) = coefficients of p(x, n) where p(x,n) = (x+1)*p(x, n-1) + n*(n-1)*x*p(x, n-2), read by rows.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle T(n, k) = coefficients of p(x, n) where p(x,n) = (x+1)*p(x, n-1) + n*(n-1)*x*p(x, n-2), read by rows.
- 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-277513a799454d97· JSON- Operation
- Image under a real-rootedness preserver
{ "index_shift": 0, "operation": "preserver_image", "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
preserver_image, SHA-256de9e497bc8e6c2b23973ae31b8d29cebbfb74787470c8a8197498f42aba0b465, 12,675 bytes (2,999 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-08ac2c6d9914754c(one_signed_coefficients)n-08ac2c6d9914754c(hadamard_kernel)n-08ac2c6d9914754c(real_rooted)