Timeline for Reference for group-algebra/exp-log like identites in combinatorics
Current License: CC BY-SA 4.0
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| Sep 4, 2023 at 13:32 | comment | added | Sam Hopkins | So more generally if we have two formal power series $A(x)=\sum_{n \geq 1} a_n x^n$, $B(x) = \sum_{n \geq 1} b_n x^n$ that are compositional inverses $A^{\langle -1 \rangle} = B$, then we get the same formula $g_n = \sum_{(c_1,\ldots,c_k)\models n} a_k f_{c_1} \cdots f_{c_k} \Leftrightarrow f_n = \sum_{(c_1,\ldots,c_k)\models n} b_k g_{c_1} \cdots g_{c_k}$. The case from the question-asker is given by taking $A(x) = e^x - 1$ and $B(x) = \log(x+1)$. | |
| Sep 2, 2023 at 2:11 | history | edited | LSpice | CC BY-SA 4.0 |
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| Sep 1, 2023 at 19:27 | history | answered | Qiaochu Yuan | CC BY-SA 4.0 |