Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013611
- Concludes
- basis_map_A013611 of Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n.
- Premises
- Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-2cd7c3e5473a248e· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013611", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-25669b349d3d4e8220498ea2febd4e4711356b8ea067ffd89ba7e7aa234ffa44a7f, 7,657 bytes (1,703 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-126effb6ce513816(real_rooted)n-126effb6ce513816(one_signed_coefficients)n-126effb6ce513816(hadamard_kernel)