How do you represent a Pivot Table (as per Excel) as a mathematical mapping using set theory?

My assumption would be you're basically mapping a Cartesian Product to a count function. However, specifying the count function is where I'm unsure. This is my best attempt at doing one for a count pivot table (averages, sums etc. could be easily tweaked):

$$ C = \{a_i \in \text{Type 1}\} \times \{b_i \in \text{Type 2}\} $$

$$ Rows = \{r_i \in C\} $$

$$ C \mapsto \sum^{|Rows|}_{i=1} c()\text{, where } c() = \begin{cases} 1,& Row_i = (a_i, b_i)\\ 0,& Row_i \neq (a_i, b_i)\end{cases}$$

Is there a simpler way, or clearer more rigorous way?

How can you explicitly declareRows as a multiset?

Full disclosure, my university was pretty bad at providing a good set theoretic background. So my apologies.


For each column in a table, there is some set it takes its values from. For example, one column could consist of arbitrary real numbers - the set $\Bbb R$, another column could be a fixed list of possible values of arbitrary type: $\{$East, West, South, North$\}, \{$Doris, Kirsten, Scot, Gerry, Lori$\}$, etc. Label the set for column number $c$ as $S_c$.

A Table of size $n$ subordinate to the set sequence $(S_c)_{c=1}^m$ is then a function $$T : \{1,2, ..., n\}\times\{1,2, ..., m\} \to \bigcup_{c=1}^m S_c$$ that satisfies the condition that for all $r$ and $c, T(r,c) \in S_c$.

Let $\mathscr T((S_c)_{c=1}^m)$ be the collection of all tables (of any size) subordinate to $(S_c)_{c=1}^m$. If $(\hat S_c)_{c=1}^k$ is another collection of sets, then a Pivot Table is simply a map $$PT: \mathscr T((S_c)_{c=1}^m) \to \mathscr T((\hat S_c)_{c=1}^k)$$

that is, it is some established method of converting a table subordinate to $(S_c)_{c=1}^m$ into a table subordinate to $(\hat S_c)_{c=1}^k$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.