Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- reversal of Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*10^j.
- Premises
- Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*10^j.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*10^j.
- 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-13ae4798662a2199· 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-256ee69a2af10f3ba6d71198b6da256ada716533a7a9c5c5be5e4d3164ef45f163f, 7,941 bytes (2,307 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-84ca83da96405582(real_rooted)n-84ca83da96405582(one_signed_coefficients)n-84ca83da96405582(hadamard_kernel)