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I'm looking for help getting Mathematica code to construct diagrammatic expressions like the following, obtained by River Li as a way to compute $\operatorname{Tr}(A^2 (A^T)^2)$ for $d\times d$ matrix $A$ with IID Gaussian entries.

The clearest explanation of such diagrams is given in Terry Tao's RMT book, Section 2.3.4.

He describes diagrammatic procedure for computing $E\operatorname{Tr}A^4$:

Which gives 4 different diagram types, that can be visualized method like above.

I'd like a method which takes an expression like $E \operatorname{Tr}(AAAA'A'A')$ where $A$ is a $d\times d$ matrix with IID standard normal entries, and generates a table of corresponding diagrams, like this, hand-derived by River Li.

Background

For the last 4 years I've been slowly organizing Mathematica-related code that helps explain Gaussian expectations (starting with 2020 post cumulants vis , also post on wicks brackets, partition lattice). I'm estimating I'm about halfway done to a nice Wolfram Community post on combinatorics of random matrices.

I'm looking for help getting Mathematica code to construct diagrammatic expressions like the following, obtained by River Li as a way to compute $\operatorname{Tr}(A^2 (A^T)^2)$ for $d\times d$ matrix $A$ with IID Gaussian entries.

The clearest explanation of such diagrams is given in Terry Tao's RMT book, Section 2.3.4.

He describes diagrammatic procedure for computing $E\operatorname{Tr}A^4$:

Which gives 4 different diagram types, that can be visualized method like above.

I'd like a method which takes an expression like $E \operatorname{Tr}(AAAA'A'A')$ where $A$ is a $d\times d$ matrix with IID standard normal entries, and generates a table of corresponding diagrams, like this, hand-derived by River Li.

Background

For the last 4 years I've been slowly organizing Mathematica-related code that helps explain Gaussian expectations (starting with 2020 post cumulants vis , also post on wicks brackets, partition lattice). I'm estimating I'm about halfway done to a nice Wolfram Community post on combinatorics of random matrices.

Cross-posted to Wolfram Community, for more visibility from WRI employees

I'm looking for help getting Mathematica code to construct diagrammatic expressions like the following, obtained by River Li as a way to compute $\operatorname{Tr}(A^2 (A^T)^2)$ for $d\times d$ matrix $A$ with IID Gaussian entries.

The clearest explanation of such diagrams is given in Terry Tao's RMT book, Section 2.3.4.

He describes diagrammatic procedure for computing $E\operatorname{Tr}A^4$:

Which gives 4 different diagram types, that can be visualized method like above.

I'd like a method which takes an expression like $E \operatorname{Tr}(AAAA'A'A')$ where $A$ is a $d\times d$ matrix with IID standard normal entries, and generates a table of corresponding diagrams, like this, hand-derived by River Li.

Background

For the last 4 years I've been slowly organizing Mathematica-related code that helps explain Gaussian expectations (starting with 2020 post cumulants vis , also post on wicks brackets, partition lattice). I'm estimating I'm about halfway done to a nice Wolfram Community post on combinatorics of random matrices.

I'm looking for help getting Mathematica code to construct diagrammatic expressions like the following, obtained by River Li as a way to compute $\operatorname{Tr}(A^2 (A^T)^2)$ for $d\times d$ matrix $A$ with IID Gaussian entries.

The clearest explanation of such diagrams is given in Terry Tao's RMT book, Section 2.3.4.

He describes diagrammatic procedure for computing $E\operatorname{Tr}A^4$:

Which gives 4 different diagram types, that can be visualized method like above.

I'd like a method which takes an expression like $E \operatorname{Tr}(AAAA'A'A')$ where $A$ is a $d\times d$ matrix with IID standard normal entries, and generates a table of corresponding diagrams, like this, hand-derived by River Li.

Background

For the last 4 years I've been slowly organizing Mathematica-related code that helps explain Gaussian expectations (starting with 2020 post cumulants vis , also post on wicks brackets, partition lattice). I'm estimating I'm about halfway done to a nice Wolfram Community post on combinatorics of random matrices.

I'm looking for help getting Mathematica code to construct diagrammatic expressions like the following, obtained by River Li as a way to compute $\operatorname{Tr}(A^2 (A^T)^2)$ for $d\times d$ matrix $A$ with IID Gaussian entries.

The clearest explanation of such diagrams is given in Terry Tao's RMT book, Section 2.3.4.

He describes diagrammatic procedure for computing $E\operatorname{Tr}A^4$:

Which gives 4 different diagram types, that can be visualized method like above.

I'd like a method which takes an expression like $E \operatorname{Tr}(AAAA'A'A')$ where $A$ is a $d\times d$ matrix with IID standard normal entries, and generates a table of corresponding diagrams.

Background

For the last 4 years I've been slowly organizing Mathematica-related code that helps with Gaussian expectations (starting with 2020 post here, also post on wicks brackets, cumulants vis, partition lattice). I'm estimating I'm about halfway done to a nice Wolfram Community post on combinatorics of random matrices.

I'm looking for help getting Mathematica code to construct diagrammatic expressions like the following, obtained by River Li as a way to compute $\operatorname{Tr}(A^2 (A^T)^2)$ for $d\times d$ matrix $A$ with IID Gaussian entries.

The clearest explanation of such diagrams is given in Terry Tao's RMT book, Section 2.3.4.

He describes diagrammatic procedure for computing $E\operatorname{Tr}A^4$:

Which gives 4 different diagram types, that can be visualized method like above.

I'd like a method which takes an expression like $E \operatorname{Tr}(AAAA'A'A')$ where $A$ is a $d\times d$ matrix with IID standard normal entries, and generates a table of corresponding diagrams, like this, hand-derived by River Li.

Background

For the last 4 years I've been slowly organizing Mathematica-related code that helps explain Gaussian expectations (starting with 2020 post cumulants vis , also post on wicks brackets, partition lattice). I'm estimating I'm about halfway done to a nice Wolfram Community post on combinatorics of random matrices.