# Types, Tokens, and Hapaxes: A New Heap's Law

arXiv: https://arxiv.org/abs/1901.00521 · HTML: https://mlsanity.com/paper/1901.00521/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2018.

## Built on by (most cited first, 4 of 4)

- [Corrections of Zipf's and Heaps' Laws Derived from Hapax Rate Models](https://mlsanity.com/paper/2307.12896/) (2023)
- [From Zipf's Law to Neural Scaling through Heaps' Law and Hilberg's Hypothesis](https://mlsanity.com/paper/2512.13491/) (2025)
- [Quadratic Term Correction on Heaps' Law](https://mlsanity.com/paper/2511.14683/) (2025)
- [From Press to Pixels: Evolving Urdu Text Recognition](https://mlsanity.com/paper/2505.13943/) (2025)

## Abstract (arXiv)

Heap's Law states that in a large enough text corpus, the number of types as a function of tokens grows as N=KMβ for some free parameters K,β. Much has been written about how this result and various generalizations can be derived from Zipf's Law. Here we derive from first principles a completely novel expression of the type-token curve and prove its superior accuracy on real text. This expression naturally generalizes to equally accurate estimates for counting hapaxes and higher n-legomena.