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Everything about Bijection
One-to-one correspondence
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set is the image of exactly one element of the first set. Given a function, the image of an element is the element in the codomain. The pre-image of an element is any element in the domain such that. Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: BijectionA 5-minute orientation
- Skim a recent paper: A bijection for tuples of commuting permutations and a log-concavity conjectureInfluential work since 2022
- Pick up a classic book: Galois theories of linear difference equationsThe most-reprinted book on the subject
- Read the landmark paper: VARIABLES AND THE BIJECTION PRINCIPLECited 94 times
- Go sideways: Surjective functionA closely related topic
- Go sideways: Bijection, injection and surjectionA closely related topic
📖 Definitions
Noun A one-to-one correspondence, a function which is both a surjection and an injection.
🏆 Landmark papers (most cited)
VARIABLES AND THE BIJECTION PRINCIPLE
The bijection from data to parameter space with the standard DEB model quantifies the supply–demand spectrum
A Rogers-Ramanujan bijection
A Bijection for Rooted Maps on Orientable Surfaces
A bijection between Littlewood-Richardson tableaux and rigged configurations
A bijection between ordered trees and 2-Motzkin paths and its many consequences
The scaling limit of uniform random plane maps, via the Ambjørn–Budd bijection
Crystal interpretation of Kerov–Kirillov–Reshetikhin bijection
🆕 Influential since 2022
A bijection for tuples of commuting permutations and a log-concavity conjecture
The Canonical Bijection between Pipe Dreams and Bumpless Pipe Dreams
Symmetric property and the bijection between perfect matchings and sub-hypercubes of enhanced hypercubes
A bijection between m-cluster-tilting objects and (m + 2)-angulations in m-cluster categories
First-passage percolation in random planar maps and Tutte’s bijection
📚 Books worth reading
- 📕Galois theories of linear difference equationsCharlotte Hardouin · 2016
- 📕Ramanujan 125Krishnaswami Alladi, Frank Garvan · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Surjective function In mathematics, a surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's…
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- Injective function In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct…
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