Integer Partitions
نویسنده
چکیده
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+1
منابع مشابه
Stirling number of the fourth kind and lucky partitions of a finite set
The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.
متن کاملk-Efficient partitions of graphs
A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
متن کاملA Product of Integer Partitions
I present a bijection on integer partitions that leads to recursive expressions, closed formulae and generating functions for the cardinality of certain sets of partitions of a positive integer n. The bijection leads also to a product on partitions that is associative with a natural grading thus defining a free associative algebra on the set of integer partitions. As an outcome of the computati...
متن کاملThe Double-complete Partitions of Integers
Representing a positive integer in terms of a sum of smaller numbers with certain conditions has been studied since MacMahon [5] pioneered perfect partitions. The complete partitions is in this category and studied by the second author [6]. In this paper, we study complete partitions with more specified completeness, which we call the double-complete partitions.
متن کاملFast Algorithms for Generating Integer Partitions
We present two new algorithms for generating integer partitions in the standard representation. They generate partitions in lexicographic and antilexicographic order, respectively. We prove that both algorithm generate partitions with constant average delay, exclusive of the output. The performance of all known integer partition algorithms is measured and compared, separately for the standard a...
متن کاملLarge deviations for integer partitions
We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation principle, of speed p n. The proof, based on projective limits, uses the representation of the uniform measure on partitions by means of suitably conditioned independent variables.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007