Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013609 of Triangle read by rows, Stirling cycle numbers of order 2, T(n, n) = 1, T(n, k) = 0 if k < 0 or k > n, otherwise T(n, k) = T(n-1, k-1) + (n…
- Premises
- Triangle read by rows, Stirling cycle numbers of order 2, T(n, n) = 1, T(n, k) = 0 if k < 0 or k > n, otherwise T(n, k) = T(n-1, k-1) + (n-…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows, Stirling cycle numbers of order 2, T(n, n) = 1, T(n, k) = 0 if k < 0 or k > n, otherwise T(n, k) = T(n-1, k-1) + (n-…
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-f2e5b103bb8c2a3c· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-256fa925279480ec894365d4c94520a0618a110b555bdbe0d178eea75e652141690, 7,708 bytes (1,719 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-3255c4dcfe77aa0b(real_rooted)n-3255c4dcfe77aa0b(one_signed_coefficients)n-3255c4dcfe77aa0b(hadamard_kernel)