Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver affine, shift 0
- Concludes
- basis_map_A013611 of Triangle whose (i,j)-th entry is 5^(i-j)*binomial(i,j).
- Premises
- basis_map_A013609 of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013609 of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed…
- Theorem
- polytool ?
- Lean
- RealRooted
Polynomial.Splits.comp_of_degree_le_one - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-a1191030326bd6b8· JSON- Operation
- Image under a real-rootedness preserver
{ "index_shift": 0, "operation": "preserver_image", "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "-1" } } }{ "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }- Certificate
preserver_image, SHA-25667cac41585d536a0fc1e6a3ff4967479173a6a4056b686cf606457bbea736ae2, 9,302 bytes (2,716 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-408f7506d6594551(one_signed_coefficients)n-408f7506d6594551(hadamard_kernel)n-408f7506d6594551(real_rooted)n-408f7506d6594551(interlacing)