Abstract
You may have wondered why the numbers \(\left( {\begin{array}{c}n\\ k\end{array}}\right) \) are called binomial coefficients, and not the “choice numbers” or “combination numbers” or something related to subsets. Why “binomial”? We’ll see why in this chapter, which begins a theme for us: encoding combinatorial results algebraically.
“Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.”
–George Pólya
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- 1.
Some might make the case that it’s the other way around: that combinatorics exists to capture algebraic information. This is also true, but harder to appreciate until one has seen a good deal of abstract algebra.
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Petersen, T.K. (2019). The Binomial Theorem. In: Inquiry-Based Enumerative Combinatorics. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-18308-0_4
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DOI: https://doi.org/10.1007/978-3-030-18308-0_4
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