What is the number of partitions of $n\in \mathbb{N}$ so that the largest part is at most $k$?
I tried it for a few small cases, but I am unable to find a general way.
2026-04-01 19:39:06.1775072346
Number of partitions of a positive integer with largest part not exceeding k
28 Views Asked by user948104 https://math.techqa.club/user/user948104/detail AtRelated Questions in INTEGER-PARTITIONS
- What form does the Law of Total Probability take if the partition you use is generated by the random variable Y?
- Permutation induced by a partition
- Number of positive integral solutions of $a+b+c+d+e=20$ such that $a<b<c<d<e$ and $(a,b,c,d,e)$ is distinct
- On a theorem (1.7) in Macdonald's Symmetric Functions and Hall Polynomials
- Asymptotic behavior of the number of ways a real plane curve of degree $n$ can intersect a real line
- Sum of the hook-lengths of a partition $\lambda$
- On an example in Macdonald's Symmetric Functions and Hall Polynomials on Paritions and their Frobenius Notation
- To show that $\sum_{x \in \lambda}(h(x)^2 - c(x)^2)=|\lambda|^2$, $h(x)$ is hook-length & $c(x)$ content of $x$, a block in the diagram of $\lambda$
- Decompose the permutation module $M^{(2, 2)}$ into irreducible representations.
- What does s(n) = s(n) mean?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?