New upper bounds for the number of partitions into a given number of parts
نویسندگان
چکیده
منابع مشابه
Identities Relating the Number of Partitions into an Even and Odd Number of Parts
If / > 0 and n > 1, let qf (n) denote the number of partitions of/? into an even number of parts, where each part occurs at most / times and Set qf(n) denote the number of partitions of n into an odd number of parts, where each part occurs at most/times. \ii>0, \etqf(0)= 1 andqf(0) = 0. For/ >Oandn > 0, \v\Aj(n) = qJ(n)-q°(n). For/= 1, it is well known [1] that , A (n) = I ~ i f n = f ^ orsome ...
متن کاملSome lower bounds for the $L$-intersection number of graphs
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
متن کاملBounds on the restrained Roman domination number of a graph
A {em Roman dominating function} on a graph $G$ is a function$f:V(G)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}A {em restrained Roman dominating}function} $f$ is a {color{blue} Roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} The wei...
متن کاملOn the Number of Parts of Integer Partitions Lying in given Residue Classes
Improving upon previous work [3] on the subject, we use Wright’s Circle Method to derive an asymptotic formula for the number of parts in all partitions of an integer n that are in any given arithmetic progression.
متن کاملNew results on upper domatic number of graphs
For a graph $G = (V, E)$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_k}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ or both for every $V_i, V_j in pi$, whenever $i neq j$. The textit{upper domatic number} $D(G)$ is the maximum order of an upper domatic partition. We study the properties of upper domatic number and propose an up...
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: Journal of Number Theory
سال: 2014
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.03.015