combinatorics.in

Manjil P. Saikia · Ahmedabad University

Courses in combinatorics and related topics.

Home for the combinatorics courses taught by Manjil P. Saikia at Ahmedabad University and elsewhere.

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A plane partition in a 5×5×5 box, reshuffling by random lozenge flips.

Courses

Total: 6 courses.

Courses include combinatorics courses taught at Ahmedabad University, summer courses for school students and open online courses.

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 →

All 6 courses →

A note on how the courses fit together

MAT631 is a sequel to MAT315/515 Combinatorial Enumeration, and MAT730 is a sequel to MAT631. In each case the earlier course is recalled rather than assumed, so you can enter at any point. Different iterations of the same course will contain new materials.

MAT 315 / 515EnumerationMAT 631Algebraic Comb.MAT 730Comb. Rep. Theory