# Questions tagged [relation-algebra]

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9 questions
1answer
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### Generalizing cycle/pseudo-tree factorizations for permutations/transformations to arbitrary binary relations

It's well known every permutation has a unique factorization into disjoint cycles (up to a re-ordering of these factors since they commute), while similarly it can be shown that every transformation ...
1answer
471 views

### Given any finite relation $R$ what is the cardinality of $\langle R\rangle=\{\underbrace{R\circ R\cdots \circ R}_{n\text{ times}}:n\in\mathbb{N}\}$?

Given any finite relation $R$ if we let $\circ$ denote relation composition and define $R^n=\underbrace{R\circ R\cdots \circ R}_{n\text{ times}}$ then does there exist an explicit formula for the ...
13answers
4k views

### Why is Set, and not Rel, so ubiquitous in mathematics?

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations. Why was there the necessity of singling ...
1answer
110 views