All Math Department Calculator Related Post

    Bridge and Cut Vertex Finder Enter Undirected Edges (u v) one per line: Find Bridges & Cut Vertices * Based on Tarjan’s DFS with discovery time and low values. A bridge is an edge whose removal increases components. A cut vertex increases components when removed. About the Bridge and Cut Vertex Finder The […]

    Incidence Graph Generator Enter Blocks (one per line, elements space-separated): Layout Style: Force-DirectedBipartite (Top/Bottom) Generate Incidence Graph * Based on Levi graph construction: vertices for points and lines, edges for incidence. Also known as the incidence graph of a set system. About the Incidence Graph Generator The Incidence Graph Generator is a combinatorial

    Graph Laplacian Matrix Calculator Enter Undirected Edges (u v) one per line: Laplacian Type: Combinatorial L = D – ANormalized L̃ = D⁻½ L D⁻½ Calculate Laplacian Matrix * Based on L = D – A (combinatorial) or L̃ = D⁻½ L D⁻½ (normalized). Eigenvalues reveal connectivity and clustering. About the Graph Laplacian

    Strongly Connected Component Finder Enter Directed Edges (u -> v) one per line: Algorithm: Kosaraju’s AlgorithmTarjan’s Algorithm Find Strongly Connected Components * Based on Kosaraju’s (DFS twice) and Tarjan’s (single DFS with low-link) algorithms. SCCs are maximal sets with paths in both directions. About the Strongly Connected Component Finder The Strongly Connected Component

    Graph Connectivity Checker Enter Edges (u v) one per line: Analysis Method: DFS (Depth-First Search)BFS (Breadth-First Search)Union-Find (Disjoint Set)Menger’s Theorem (k-Connectivity) Check Graph Connectivity * Based on DFS/BFS traversal, Union-Find, and Menger’s theorem. A graph is connected if one component exists. About the Graph Connectivity Checker The Graph Connectivity Checker is a robust

    Ramsey Number Estimator Clique Size s (≥3): Independent Set Size t (≥3): Estimate Ramsey Number * Based on Ramsey’s theorem, probabilistic lower bounds, and known exact values. R(3,3)=6, R(5,5) ∈ [43,48]. About the Ramsey Number Estimator The Ramsey Number Estimator is a graph-theoretic tool that computes known bounds for the Ramsey number R(s,t)

    Integer Partition Generator Positive Integer n: Display Mode: List PartitionsYoung DiagramsStatistics & Conjugates Generate Integer Partitions * Based on standard descending order algorithm and conjugate partition via Young diagram transpose. About the Integer Partition Generator The Integer Partition Generator is a comprehensive combinatorial tool that enumerates all integer partitions of n — every

    Partition Number Calculator Positive Integer n: Show Range (n to n+range): Calculate Partition Numbers * Based on Euler’s pentagonal number theorem and recurrence: p(n) = Σ (-1)^{k+1} [p(n−ω(k)) + p(n−ω(−k))]. About the Partition Number Calculator The Partition Number Calculator is a mathematically precise tool that computes the partition function p(n) — the number

    Harmonic Number Calculator Positive Integer n: Decimal Precision: Calculate Harmonic Number * Based on digamma function ψ(n+1) = H(n) − γ and Euler-Maclaurin summation. γ ≈ 0.5772156649015328606. About the Harmonic Number Calculator The Harmonic Number Calculator is a precision mathematical tool that computes the nth harmonic number H(n) = 1 + 1/2 +

    Bernoulli Number Calculator Index n (0 ≤ n ≤ 1000): Show Range (n to n+range): Calculate Bernoulli Numbers * Based on Akiyama–Tanigawa algorithm (1999), von Staudt–Clausen theorem, and zeta(1−k). B₁ = −1/2 (modern convention). About the Bernoulli Number Calculator The Bernoulli Number Calculator is a mathematically rigorous tool that computes Bernoulli numbers B(n)