The lattice of integer partitions
نویسندگان
چکیده
منابع مشابه
0 The lattice of integer partitions and its infinite extension
In this paper, we use a simple discrete dynamical system to study integers partitions and their lattice. The set of reachable configurations equiped with the order induced by the transitions of the system is exactly the lattice of integer partitions equiped with the dominance ordering. We first explain how this lattice can be constructed, by showing its self-similarity property. Then, we define...
متن کاملThe lattice of integer partitions and its infinite extension
In this paper, we use a simple discrete dynamical system to study integers partitions and their lattice. The set of reachable configurations equiped with the order induced by the transitions of the system is exactly the lattice of integer partitions equiped with the dominance ordering. We first explain how this lattice can be constructed, by showing its self-similarity property. Then, we define...
متن کاملThe Lattice of Integer Partitions and Its Innnite Extension
In this paper, we use a simple discrete dynamical system to study integers partitions and their lattice. The set of reachable conngurations equiped with the order induced by the transitions of the system is exactly the lattice of integer partitions equiped with the dominance ordering. We rst explain how this lattice can be constructed, by showing its self-similarity property. Then, we deene a n...
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Let denote the positive octant of the regular -dimensional cubic lattice. Each vertex (1 2 ) of is adjacent to all vertices of the form (1 2 + 1 ), 1 ≤ ≤ . A -partition of a positive integer is an assignment of nonnegative integers 12 to the vertices of , subject to both an ordering condition 12 ≥ max 1≤≤ 12+...
متن کاملSubsums of Integer Partitions
Abstract For integer partitions λ : n = a1 + ...+ ak, where a1 ≥ a2 ≥ . . . ≥ ak ≥ 1, we study the sum a1 + a3 + . . . of the parts of odd index. We show that the average of this sum, over all partitions λ of n, is of the form n/2 + ( √ 6/(8π)) √ n log n+ c2,1 √ n+O(log n). More generally, we study the sum ai + am+i + a2m+i + . . . of the parts whose indices lie in a given arithmetic progressio...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1973
ISSN: 0012-365X
DOI: 10.1016/0012-365x(73)90094-0