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1 Elementary Combinatorics 1 [1] The number of subsets of an n-element set is 2n 2 [1] A composition of n is a sequence α = (α 1α 2 αk) of positive integers such that P αi= n The number of compositions of n is 2n−1 3 [2] The total number of parts of all compositions of n is equal to (n+1)2n−2 4

  • Which bijective proof is known for the case i = 0?

    . (n + i + 1)(2n + 2i + 1) i n A (difficult) bijective proof is known for the case i = 0. 239. Let f(n) be the number of n-elements subsets S of N N with the following properties. ×

  • Which proofs are bijectively counted by (7)?

    We give here a subset of these interpretations that are the most fundamental or most interesting. Prob-lem 164 is perhaps the easiest one to show bijectively is counted by (7). All your other proofs should be bijections with previously shown “Catalan sets.”

  • How do you find bijections?

    There are certain refinements of the numbers (a)–(d) which may be useful in finding bijections. For instance, it appears that the number of descending plane partitions with largest part at most n and with exactly k parts equal to n is equal to the number of monotone triangles of length n and bottom element k + 1.

[Proof] Function is bijective

[Proof] Function is bijective

Bijection Proof (a taste of math proof)

Bijection Proof (a taste of math proof)

Bijective Functions and Why Theyre Important  Bijections Bijective Proof Functions and Relations

Bijective Functions and Why Theyre Important Bijections Bijective Proof Functions and Relations

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