${n \choose k}$: the number of $k$-length subsets of a set with length $n$.

Multisets: Sets without uniqueness. $t$ types of (repeatable) elements.

Number of multisets of length $n$ is ${n + t - 1 \choose t - 1}$.

Surjective: Onto. Every element in the codomain is the image of at least one element in the domain.

Injective: One-to-one.

Bijective: Both. Wires task in among us.

Formulas


Combinatorial Interpretations

Bijective Proofs

Inclusion/Exclusion

Generating Series

Compositions

Binary Strings & Regular Expressions

Excluded Substrings


Recurrence Relations

Homogeneous Linear Recurrence Relations