Balanced Partitions of Trees and Applications
โ Scribed by Feldmann, Andreas Emil; Foschini, Luca
- Book ID
- 120910106
- Publisher
- Springer
- Year
- 2013
- Tongue
- English
- Weight
- 896 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0178-4617
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The partitions of a natural number n (with parts taken in non-increasing order), may be listed in dictionary order. This ordering of partitions is shown to correspond to the post ordering of chains of a finite tree T[n]. It is shown that T[n] belongs to a, the class of normal trees. % occurs indepen
Let d, r โ N and โข be any norm on R d . Let B denote the unit ball with respect to this norm. We show that any sequence v 1 , v 2 , . . . of vectors in B can be partitioned into r subsequences V 1 , . . ., V r in a balanced manner with respect to the partial sums: For all n โ N, r, we have i k,v i โ
We give a simple and natural proof of (an extension of) the identity P(X. 1. )I ) = t-'2( X I. I -I. II --I ). The number P(li, I, 17) counts noncrossing partitions of { I, 2. I} unto II parts such that no part contains two numbers .Y and J'. O<.v --.v<k. The lower index 2 indicate\ partitions with
We present observations and problems connected with a weighted binary tree representation of integer partitions. ๏ฃฉ 2002 Elsevier Science (USA)