EXERCISES ( without solutions ) for Chapter 7 ( symmetric functions ) of Enumerative Combinatorics
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چکیده
1. [2] Find the number f (n) of pairs (λ, µ) such that λ ⊢ n and µ covers λ in Young's lattice Y. Express your answer in terms of p(k), the number of partitions of k, for certain values of k. Try to give a direct bijection, avoiding generating functions, recurrence relations, induction, etc.
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EXERCISES ( without solutions ) for Chapter 7 ( symmetric functions ) of
1. [2] Find the number f (n) of pairs (λ, µ) such that λ ⊢ n and µ covers λ in Young's lattice Y. Express your answer in terms of p(k), the number of partitions of k, for certain values of k. Try to give a direct bijection, avoiding generating functions, recurrence relations, induction, etc.
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