Counting Paths in Young’s Lattice

@inproceedings{Gessel1993CountingPI,
  title={Counting Paths in Young’s Lattice},
  author={Ira M. Gessel and Ma},
  year={1993}
}
Young’s lattice is the lattice of partitions of integers, ordered by inclusion of diagrams. Standard Young tableaux can be represented as paths in Young’s lattice that go up by one square at each step, and more general paths in Young’s lattice correspond to more general kinds of tableaux. Using the theory of symmetric functions, in particular Pieri’s rule for multiplying a Schur function by a complete symmetric function, we derive formulas for counting paths in Young’s lattice that go up or… CONTINUE READING
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