Construct · 1 fields · 3 citations

pigeonhole principle: a standalone construct

One name. One construct. A landmark on the map.

● anchor · a standalone principle Nearest construct by meaningarrangementcompare the meanings
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pigeonholeprinciple1 CONSTRUCTPigeonholeDIRICHLET · BOX PRINCIPLE

A single standalone construct; nearby constructs are located against it in the Collider. Tap a field for its definition, unit, and measures.

Combinatorics

The principle that more items than containers forces a shared container

The pigeonhole principle is the observation that if n items are placed into m containers and n is greater than m, then at least one container must hold more than one item. Historians trace an informal statement to a 1622 collection of mathematical recreations by the Jesuit writer Jean Leurechon, and the principle took its standard formal name from Peter Gustav Lejeune Dirichlet, who by the 1830s was calling it the Schubfachprinzip, German for drawer principle, from which come the English names Dirichlet's box principle and Dirichlet's drawer principle (Rittaud and Heeffer, 2014). Its general form states that distributing n objects among m boxes forces some box to contain at least the ceiling of n divided by m objects. What makes it a landmark is its reach relative to its simplicity: a one-line counting fact underwrites existence proofs across combinatorics, number theory, and geometry, guaranteeing that some configuration must occur without exhibiting it, as in the standard results collected in van Lint and Wilson (2001) and Aigner and Ziegler (2018).[1][2][3]

Unit
A combinatorial existence principle: a statement guaranteeing a repeated assignment whenever objects outnumber the categories they fall into
Recovery means
Not applicable
Measured by
Applied as a proof technique: with n objects placed in m categories and n greater than m, at least one category is shown to hold at least the ceiling of n divided by m objects

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Nearby constructs

injection3 fields · 3 citationsjingle · one word, three constructsset3 fields · 5 citationsjingle · one word, three constructsproof2 fields · 5 citationsjingle · one word, two constructs

References

  1. Rittaud, B., & Heeffer, A. (2014). The pigeonhole principle, two centuries before Dirichlet. The Mathematical Intelligencer, 36(2), 27–29. https://doi.org/10.1007/s00283-013-9389-1
  2. Aigner, M., & Ziegler, G. M. (2018). Proofs from THE BOOK (6th ed.). Springer. https://doi.org/10.1007/978-3-662-57265-8
  3. van Lint, J. H., & Wilson, R. M. (2001). A course in combinatorics (2nd ed.). Cambridge University Press. https://doi.org/10.1017/CBO9780511987045

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