Stories about groups and sequences
It is well known that a number of problems in combinatorial theory are closely related to group actions on partially ordered sets (usually on Boolean lattices). This ties together disperate themes from enumeration theory of Pólya, invariant theory, Ramsey theory, commutative algebra, representation theory of symmetric groups, reconstruction problems, etc. This interesting article is a collection of short ``stories'' devoted to such subjects as: 1. Two-graphs and even graphs. 2. Groups and counting. 3. An inequality and a Ramsey problem. 4. Direct and wreath products. 5. N-free graphs and posets. 6. Algebraic interlude. 7. Reconstruction. 8. Cycle index. 9. A product identity. 10. Stirling numbers. 11. Stabilisers and derivatives. 12. The probability of connectedness. 13. Two-graphs revisited. Note that there is a corrected reprint of the paper.
scientific article; zbMATH DE number 994658
scientific article