Discrete Mathematics
Graph theory, combinatorics, binomial coefficients, Catalan numbers, recurrences, inclusion–exclusion, chromatic numbers, generating functions, Stirling numbers, and partitions.
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Binomial Coefficient Calculator
Calculate nCr and nPr values with Pascal's triangle row visualization.
Catalan Number Calculator
Calculate Catalan numbers and their combinatorial interpretations including binary trees and lattice paths.
Chromatic Number Estimator
Estimate the chromatic number of a graph using Brook's theorem and greedy coloring bounds.
Permutations & Combinations Calculator
Calculate permutations and combinations with or without repetition for any n and r values.
Sequence Analyzer & Generating Function
Analyze a sequence to detect arithmetic, geometric, or polynomial patterns and predict the next term.
Graph Theory Calculator
Analyze graph properties including degree, density, connectivity, and Eulerian path possibility.
Inclusion-Exclusion Calculator
Apply the inclusion-exclusion principle to compute union sizes and exclusive membership for up to three sets.
Integer Partition Calculator
Count the number of integer partitions of n with optional constraints on maximum part size and distinctness.
Recurrence Relation Calculator
Solve linear recurrence relations a_n = p*a_{n-1} + q*a_{n-2} with given initial conditions.
Stirling Number Calculator
Calculate Stirling numbers of the first and second kind, plus Bell numbers for set partitions.