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A lattice is a partially ordered set (poset) in which any two elements have a unique supremum (the elements' least upper bound; called their join) and an infimum (greatest lower bound; called their meet).

A combination is a selection of items from a collection, such that the order of selection does not matter. Given $n$ elements and selecting $r$ at a time, the number of combinations is $C(n, r) = \frac{n!}{r!(n-r)!}$.

An algorithm is a finite sequence of well-defined instructions, typically used to solve a class of problems or perform a computation. Properties include runtime complexity and space complexity.

A graph is an ordered pair $G = (V, E)$ where $V$ is a set of vertices and $E$ is a set of edges, which are 2-element subsets of $V$. Properties include connectivity, cycles, and possibly directed or weighted edges.

A binary tree is a tree in which each node has at most two children, which are referred to as the left child and the right child. Properties include height, balance, and it is the basis for binary search trees.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Properties include determinant, rank, and can represent systems of linear equations.

A set is a well-defined collection of distinct objects. Set properties include cardinality, subsets, intersections, unions, and complements.

A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. For set size $n$, there are $n!$ possible permutations.

Recursion is a method where the solution to a problem depends on solutions to smaller instances of the same problem. A recursive function calls itself with a smaller input.

A tree is a connected graph with no cycles. Properties include having exactly $n-1$ edges for $n$ vertices, and any two vertices are connected by exactly one path.

A function $f$ from a set $X$ to a set $Y$ assigns each element of $X$ to exactly one element of $Y$. Properties include being one-to-one (injective), onto (surjective), or both (bijective).