Enumerative Combinatorics, Volume 2

Stanley, R. P., & Fomin, S. (1999). Enumerative Combinatorics, Volume 2. Cambridge University Press.

Type

Book

Intellectual base

Review or monograph

Year

1999

DOI

10.1017/cbo9780511609589

ISBN

9780521560696

Link

https://doi.org/10.1017/CBO9780511609589

Cited from

mathematics

Cited by

3 citations across 3 artifacts.

Primes

• Cycle
  • Loop integrals and conservation: the circuit-law sum around a loop, the line integral around a closed contour, and conservation of circulation share the fact that a cycle imposes a constraint on the contents of the loop. Cycles versus boundaries: homology measures closed-but-not-bounding cycles, a pattern that recurs wherever a notion of "closed but not bounding" is needed, including the structure of conservation laws. Cycle index: the cycle structure of a group action determines orbit counts under symmetry.

Domain-specific

• Murnaghan–Nakayama rule
  • Partitions index both irreducible characters and conjugacy cycle types, signs depend on rim-hook height, and the result is a recursive character computation rather than a general branching rule.
• Robinson–Schensted–Knuth correspondence
  • RSK repeatedly inserts symbols derived from matrix entries to construct an insertion tableau and a recording tableau; row and column sums determine their weights and transposition swaps the pair.

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