# Analisi Due by Gianni Gilardi PDF By Gianni Gilardi

ISBN-10: 8838607273

ISBN-13: 9788838607271

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36) 1≤ j≤H where μ is the cardinal function. 36). H denoting the set {1, 2, . . , h, . . 1 Lattice of Partition Set of a Finite Set 17 where |G| stands for card(G). μ j∈G F j is the cardinal of injective mapping sequences which cannot reach G. By setting g = card(G) and m = max1≤k≤K n k , we can observe that the latter cardinal is null if m > H − g. 38) and then, it depends only on g = card(G). 38). The sequence of injective mappings (φ1 , φ2 , . . , φk , . . , φ K ) of C1 , C2 , . . , Ck , .

Since y belongs to B(x0 ; i), y is a centre of B(x0 ; i) (see Proposition 12). Then du (y, z) = i. And, for x ∈ / B(x0 ; i), du (y, x) > i. Finally, du (x, y) = du (x, z) > du (y, z). 36 1 On Some Facets of the Partition Set of a Finite Set Algorithm Let us label the elements of the object set O. O = {o1 , o2 , . . , oi , . . , on }. To each ranking (permutation) (o(1) , o(2) , . . , o(i) , . . , row) represents the o(i) object, 1 ≤ i ≤ n. The distance value between o(i) and o( j) is set at the intersection of the ith row and the jth column, 1 ≤ i, j ≤ n.

The proportion of such partitions is given by the formula l! h∈L m h ! (n−l)! h ∈L / mh ! × n! 43) 1≤h≤H In fact, a partition Q which takes part in the counting is equivalent to an ordered pair of partitions of respective types (m h |h ∈ L) and (m h |h ∈ / L) defined on k∈M Ck and k ∈M C , respectively. 43) is deduced. 43) can be brought down to the inverse of the binomial coefficient nl . Hence the result. Proposition 5 Let P be a fixed partition of type t = (n 1 , n 2 , . . , n k , . . , n K ), the proportion of partitions Q into H non-empty classes such that P ∧ Q = Ps , of type s = (m 1 , m 2 , .