Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- reversal of Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ).
- Premises
- Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ).
- 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-72692ea5869564d5· 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-25672f4ba8748c27fc87f68a74739b0cbecd3a189730b757c3817966efc644b09b2, 13,793 bytes (3,269 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-9130684ebb51c694(real_rooted)n-9130684ebb51c694(one_signed_coefficients)n-9130684ebb51c694(hadamard_kernel)