Partitions of multi-partite numbers
نویسندگان
چکیده
منابع مشابه
A Bound for Size Ramsey Numbers of Multi-partite Graphs
It is shown that the (diagonal) size Ramsey numbers of complete m-partite graphs Km(n) can be bounded from below by cn 22(m−1)n, where c is a positive constant.
متن کاملPolytopes of partitions of numbers
We study the vertices and facets of the polytopes of partitions of numbers. The partition polytope n P is the convex hull of the set of incidence vectors of all partitions 1 2 2 ... n n x x nx = + + +. We show that the sequence 1 2 n P P P can be treated as an embedded chain. Dynamics of behavior of the vertices of n P , as n increases, is established. Some sufficient and some necessary conditi...
متن کاملPartitions into three triangular numbers
A celebrated result of Gauss states that every positive integer can be represented as the sum of three triangular numbers. In this article we study p3∆(n), the number of partitions of the integer n into three triangular numbers, as well as p3∆(n), the number of partitions of n into three distinct triangular numbers. Unlike t(n), which counts the number of representations of n into three triangu...
متن کاملCompositions, Partitions, and Fibonacci Numbers
A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the number of compositions of n + 1 into parts greater than one. Some commentary about the history of partitions and compositions is provided.
متن کاملGraphs, partitions and Fibonacci numbers
The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees with n edges and Fibonacci number > 2n−1 + 5 have diameter ≤ 4 and determine the order of these trees with respect to their Fibonacci numbers. Furthermore, it is shown that the average Fibonacci number of a star-like ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1956
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1956-0084012-x