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Dyck path Triangulation Binary tree Lodha Genius Programme

Cataland

One sequence — 1, 2, 5, 14, 42 — and the hundreds of objects it counts. Daily lectures and workshops.

Grades 11–12Daily 09:00–12:002026Archive Course page → Graduate topics

Combinatorics of Permutations

Permutation statistics and q-analogues on one side, pattern avoidance on the other.

GraduateStatistics & patternsCurrent Course page → 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A 5 by 5 alternating sign matrix as a square-ice configuration A five by five square lattice with an arrow on every edge. Boundary arrows point inward on the left and right and outward on the top and bottom. Nine vertices are marked with a plus and four with a minus, giving the alternating sign matrix with 1 in the centre of the first and last rows and alternating entries forming a diamond. Graduate topics

Enumeration of Alternating Sign Matrices

Square ice and determinant evaluations on one side, symmetry classes and refined enumeration on the other.

GraduateSix-vertex & symmetryCurrent Course page → ∅ MAT730

Combinatorial Representation Theory (2025)

Representations of the symmetric group, reached through Specht modules, tableaux and symmetric functions.

GraduateMon & FriMonsoon 2025Archive Course page → Open online course

Advanced q-analysis I

Integer partitions through the lens of q-series — Euler, Jacobi, Rogers and Ramanujan, then Bailey and Andrews.

OnlineWed & SunNo certificateArchive Course page → 8 6 4 3 1 6 4 2 1 3 1 1 MAT631

Algebraic Combinatorics (2025)

Tableau combinatorics and symmetric functions, by way of RSK and the hook-length formula.

GraduateTue & WedWinter 2025Archive Course page →