Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013610
- Concludes
- reversal of Riordan array (1, 3+3x).
- Premises
- Triangle read by rows: T(n,k) is the number of ternary words (i.e., finite sequences of 0's, 1's and 2's) of length n having k occurrences …
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangle read by rows: T(n,k) is the number of ternary words (i.e., finite sequences of 0's, 1's and 2's) of length n having k occurrences …
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-830e82d9cb2159c9· 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": 1, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-256a391cee560f3fcd48c9b76bc948abe7a2c1f962df8606c97d56395473e64bc0d, 14,522 bytes (2,901 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-0515531ee2138839(real_rooted)n-0515531ee2138839(one_signed_coefficients)n-0515531ee2138839(hadamard_kernel)n-0515531ee2138839(interlacing)