Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013610
- Concludes
- basis_map_A013610 of Triangle read by rows: T(n,0)=1, T(n,n)=2, T(n,m) = T(n-1,m-1) + Sum_{k=0..m} T(n-1-k,m-k).
- Premises
- Triangle read by rows: T(n,0)=1, T(n,n)=2, T(n,m) = T(n-1,m-1) + Sum_{k=0..m} T(n-1-k,m-k).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows: T(n,0)=1, T(n,n)=2, T(n,m) = T(n-1,m-1) + Sum_{k=0..m} T(n-1-k,m-k).
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-087c2053836c9fd5· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013610", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }{ "claim": "interlacing", "from_index": 2, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-256dc1dc599852a2fb0a9db24f155a0379c91d405223af48e2da43e6a2b311b0cf7, 14,208 bytes (2,668 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-c04eaa7a3fc005c1(real_rooted)n-c04eaa7a3fc005c1(one_signed_coefficients)n-c04eaa7a3fc005c1(hadamard_kernel)n-c04eaa7a3fc005c1(interlacing)