Concept Encyclopedia

Reference for mathematical tools used in quant interview problems. Linked from practice explanations and hints.

Permutations where no element appears in its original position.

Catalan Numbers

Count balanced parentheses, binary trees, non-crossing partitions, and lattice paths.

Burnside's Lemma

Count distinct objects under symmetry by averaging fixed points over the symmetry group.

Vandermonde Identity

Splits a combination across two groups: C(m+n, r) = sum of C(m,k)C(n,r-k).

Pigeonhole Principle

If n+1 objects go into n boxes, at least one box holds two or more.

Stirling Numbers (Second Kind)

S(n,k) counts ways to partition n objects into exactly k non-empty groups.

Count ways to put n identical balls into k distinct bins: C(n+k-1, k-1).

Inclusion-Exclusion Principle

Compute the probability of a union by alternating sums of intersections.

Linearity of Expectation

E[X+Y] = E[X] + E[Y], always — even when X and Y are dependent.

Coupon Collector Problem

Expected draws to complete a set of n types: n * H_n ≈ n ln(n).

Reflection Principle

Count lattice paths that cross a boundary by reflecting the path at the first crossing point.

Markov's Inequality

For non-negative X: P(X >= a) <= E[X]/a — crude but universal tail bound.

Showing 1–12 of 50

Page 1 of 5