Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 3*x + 5.
- Premises
- Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 3*x + 5.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 3*x + 5.
- 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-6e04fc01636b38e0· 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-2569c933a4ee2f697a4a8e81ea5caa49ac7539abc0736eb1f8f59c334ed56a18179, 10,692 bytes (2,714 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-f3a4ae052af3da90(one_signed_coefficients)n-f3a4ae052af3da90(hadamard_kernel)n-f3a4ae052af3da90(real_rooted)