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This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities
0
2
English
English [CC]
FREE
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Description
young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields
Course content
- Course Introduction Unlimited
- Additive Number Theory Unlimited
- Lower Bound in Schur’s Theorem Unlimited
- More on Colorings Unlimited
- More on Colorings (cont.) Unlimited
- 5-Color Theorem Unlimited
- Edge Coloring of Bipartite Graphs Unlimited
- Glauber Dynamics Unlimited
- Chromatic Polynomial Unlimited
- Acyclic Orientations Unlimited
- More on Tutte Polynomial Unlimited
- Tutte Polynomial for a Cycle Unlimited
- Crapo’s Bijection Unlimited
- Kauffman Bracket and Jones Polynomial Unlimited
- Linear Algebra Methods Unlimited
- Non-uniform Ray-Chaudhuri-Wilson Theorem Frankl-Wilson Theorem Unlimited
- Borsuk Conjecture Kahn-Kalai Theorem Unlimited
- Packing with Bipartite Graphs Unlimited
- Hamiltonicity, Basic Results Tutte’s Counter Example Unlimited
- Grinberg’s Formula Unlimited
- Tutte’s Theorem Unlimited
- Hamiltonian Cayley Graphs of General Groups Unlimited
- Menger Theorem Unlimited
- Dilworth Theorem Unlimited
- Sperner Theorem Unlimited
- Swell Colorings Unlimited
- Turán’s Theorem Unlimited
- Pattern Avoidance Unlimited
- Permutation Patterns Unlimited
- Proof by Marcus and Tardos of the Stanley-Wilf Conjecture Unlimited
- Convex Polyomino Unlimited
- Solid Partitions Unlimited
- Hook Length Formula Unlimited
- Two Polytope Theorem Unlimited
- Connection to RSK Special Cases Unlimited
- Duality Unlimited
- Direct Bijective Proof of the Hook Length Formula Unlimited
- Introduction to Tilings Unlimited
Instructor
Massachusetts Institute of Technology
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1916
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