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YCor
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Reference for Groupgroup-Algebraalgebra/exp-log like identites in Combinatoricscombinatorics

I've encountered several identities in combinatorics that resemble inversion formulas, as showshown below,

exp-log-correspondence

Here, $f_i, g_k \ \forall i,k \in \mathbb{N}$$f_i, g_k$, $\forall i,k \in \mathbb{N}$, are coefficients of some formal power series.

I noticed that the coefficients in these sums are in resemblance with coefficients in the power series of $ln(1+x), \exp{x} -1$$\ln(1+x), \exp{x} -1$, which suggests to me that they are related in some way to Lie Groupgroup - Lie Algebra Correspondencealgebra correspondence.

However, I have not been able to find any discuss any textbook(s) that deal with these identities in full generality. I even don't have a name for such 'classes' of identities.I I would really appreciate some resources that deal with this 'particular' form of identities.

Reference for Group-Algebra/exp-log like identites in Combinatorics

I've encountered several identities in combinatorics that resemble inversion formulas, as show below,

exp-log-correspondence

Here, $f_i, g_k \ \forall i,k \in \mathbb{N}$ are coefficients of some formal power series.

I noticed that the coefficients in these sums are in resemblance with coefficients in the power series of $ln(1+x), \exp{x} -1$, which suggests to me that they are related in some way to Lie Group - Lie Algebra Correspondence.

However, I have not been able to find any discuss any textbook(s) that deal with these identities in full generality. I even don't have a name for such 'classes' of identities.I would really appreciate some resources that deal with this 'particular' form of identities.

Reference for group-algebra/exp-log like identites in combinatorics

I've encountered several identities in combinatorics that resemble inversion formulas, as shown below,

exp-log-correspondence

Here, $f_i, g_k$, $\forall i,k \in \mathbb{N}$, are coefficients of some formal power series.

I noticed that the coefficients in these sums are in resemblance with coefficients in the power series of $\ln(1+x), \exp{x} -1$, which suggests to me that they are related in some way to Lie group - Lie algebra correspondence.

However, I have not been able to find any discuss any textbook(s) that deal with these identities in full generality. I even don't have a name for such 'classes' of identities. I would really appreciate some resources that deal with this 'particular' form of identities.

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total dependent random choice
total dependent random choice
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I've encountered several identities in combinatorics that resemble inversion formulas, as show below,

exp-log-correspondence

Here, $f_i, g_k \ \forall i,k \in \mathbb{N}$ are coefficients of some formal power series.

I noticed that the coefficients in these sums are in resemblance with coefficients in the power series of $ln(1+x), \exp{x} -1$, which suggests to me that they are related in some way to Lie Group - Lie Algebra Correspondence.

However, I have not been able to find any discuss any textbook(s) that deal with these identities in full generality. I even don't have a name for such 'classes' of identities.I would really appreciate some resources that deal with this 'particular' form of identities.

I've encountered several identities in combinatorics that resemble inversion formulas, as show below,

exp-log-correspondence

Here, $f_i, g_k \ \forall i,k \in \mathbb{N}$ are coefficients of some formal power series.

However, I have not been able to find any discuss any textbook(s) that deal with these identities in full generality. I even don't have a name for such 'classes' of identities.I would really appreciate some resources that deal with this 'particular' form of identities.

I've encountered several identities in combinatorics that resemble inversion formulas, as show below,

exp-log-correspondence

Here, $f_i, g_k \ \forall i,k \in \mathbb{N}$ are coefficients of some formal power series.

I noticed that the coefficients in these sums are in resemblance with coefficients in the power series of $ln(1+x), \exp{x} -1$, which suggests to me that they are related in some way to Lie Group - Lie Algebra Correspondence.

However, I have not been able to find any discuss any textbook(s) that deal with these identities in full generality. I even don't have a name for such 'classes' of identities.I would really appreciate some resources that deal with this 'particular' form of identities.

Source Link
total dependent random choice
total dependent random choice
  • 283
  • 1
  • 11

Reference for Group-Algebra/exp-log like identites in Combinatorics

I've encountered several identities in combinatorics that resemble inversion formulas, as show below,

exp-log-correspondence

Here, $f_i, g_k \ \forall i,k \in \mathbb{N}$ are coefficients of some formal power series.

However, I have not been able to find any discuss any textbook(s) that deal with these identities in full generality. I even don't have a name for such 'classes' of identities.I would really appreciate some resources that deal with this 'particular' form of identities.