Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver affine, shift 0
- Concludes
- Triangle read by rows: the reversed x = 1+q Narayana triangle at m=2.
- Premises
- Triangle read by rows: T(n,k) is the number of ternary trees with n edges and having k middle edges (n >= 0, k >= 0).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows: T(n,k) is the number of ternary trees with n edges and having k middle edges (n >= 0, k >= 0).
- Theorem
- polytool ?
- Lean
- RealRooted
Polynomial.Splits.comp_of_degree_le_one - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-0cd0209be356c72c· 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": 1, "region": { "upper": { "closed": true, "value": "-1" } } }- Certificate
preserver_image, SHA-25682bf5956c33a7a691c72faf29546eb60d468227cd03ecdfb4620b0e3f14602b1, 8,838 bytes (2,704 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-f00f6de2d4bbc6f5(hadamard_kernel)n-f00f6de2d4bbc6f5(real_rooted)n-f00f6de2d4bbc6f5(one_signed_coefficients)