par Dubois, Olivier 
;Louchard, Guy ;Mandler, Jacques
Référence Combinatorics, probability & computing, 13, 4-5, page (537-575)
Publication Publié, 2004-07
;Louchard, Guy ;Mandler, JacquesRéférence Combinatorics, probability & computing, 13, 4-5, page (537-575)
Publication Publié, 2004-07
Article révisé par les pairs
| Résumé : | An additive decomposition of a set I of nonnegative integers is an expression of I as the arithmetic sum of two other such sets. If the smaller of these has p elements, we have a p-decomposition. If I is obtained by randomly removing nα integers from {0,...,n - 1}, decomposability translates into a balls-and-urns problem, which we start to investigate (for large n) by first showing that the number of p-decompositions exhibits a threshold phenomenon as a crosses a p-dependent critical value. We then study in detail the distribution of the number of 2-decompositions. For this last case we show that the threshold is sharp and we establish the threshold function. |
