Discrete Mathematics and Its Applications¶
Rosen, K. H. (2012). Discrete Mathematics and Its Applications. McGraw-Hill.
Retired. This is not a bibliographic entry. Our extractor captured an inline prose definition from an article and stored it as a work. The concept is real; this registry record is a parsing defect. This entry is kept so the citations that pointed at it still resolve, and so the correction is visible rather than silent.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Mechanisms¶
- Collision Analysis Matrix
- Its strength is making non-injectivity concrete and located: instead of an abstract warning that a mapping might be many-to-one, it shows the exact inputs that coincide — the pigeonhole reality
This sourceDocuments whenever inputs outnumber output buckets, some column must collect more than one.
- Its strength is making non-injectivity concrete and located: instead of an abstract warning that a mapping might be many-to-one, it shows the exact inputs that coincide — the pigeonhole reality
- Equivalence-Class Partition Derivation
- The outcome is a deduplicated master list where "one person, one block" is a theorem, not a hope: nobody had to draw the boundaries or check for overlaps, because the relation's structure produced a clean partition on its own.
This sourceProves that an equivalence relation's classes cover the set and are equal or disjoint, thereby forming a partition.
- The outcome is a deduplicated master list where "one person, one block" is a theorem, not a hope: nobody had to draw the boundaries or check for overlaps, because the relation's structure produced a clean partition on its own.
- Hash Collision Check
- For any truncated or fixed-length encoding, the pigeonhole principle guarantees that a code shorter than its input space must collide for some inputs — the only open question is at what volume, not whether.
This sourceApplies the pigeonhole principle: a fixed code space smaller than the possible input space necessarily contains collisions.
- For any truncated or fixed-length encoding, the pigeonhole principle guarantees that a code shorter than its input space must collide for some inputs — the only open question is at what volume, not whether.
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Not recorded. Neither this nor any other of the 3 citations of this work carries a recorded support check.
Was it audited? Yes. A second, independent pass read the citation against the article text and recorded a verdict.
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Links previously used in the corpus¶
Before the registry existed this work was also linked 3 other ways.
- https://old.maa.org/node/106717 ×1
- https://openlibrary.org/books/OL24839122M/Discrete_mathematics_and_its_applications ×1
- https://search.worldcat.org/title/Discrete-mathematics-and-its-applications/oclc/1103788578 ×1
Registry ID ref:2dd11550c914 · see in the full table