Glossary: Other

Definitions in this project whose names start with Other. The whole glossary has the other sections.

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α def

$\alpha(n)$ is the supremum of minTriangleArea S over all sets S of $n$ points in the unit disk. · Erdos507.α

Δ def

def Δ : PowerSeries ℤ · RamanujanTau.Δ

δ def

For each $m$ and $\alpha$, $\delta (m, \alpha)$ is the density of the set of integers which are divisible by some $d \equiv 1 \pmod{m}$ with $1 < d < exp (m ^ \alpha)$ exists. · Erdos697.δ

θ def

def θ : ℝ · MovingSofa.GerversSofa.θ

κ def

Let $\kappa = (2^{\aleph_0})^+$. This is the successor cardinal of the continuum. · Erdos598.κ

μ def

Start with a set $X=\{1,2,...,n\}$ of $n$ elements and the family $2^X$ of all subsets of $X$. For a real number $p$ between zero and one, we consider a probability distribution $\mu_p$ on $2^X$ where the probability that $i \in S$ is $p$, … · Mathoverflow10799.μ

μFamily def

The $p$-biased measure of a family $\mathcal F \subseteq 2^{[n]}$, i.e. $\mu_p(\mathcal F) = \sum_{S \in \mathcal F} \mu_p(S)$. · Mathoverflow10799.μFamily

τ abbrev

abbrev τ · Erdos945.τ

τ def

def τ (n : ℕ) : ℤ · RamanujanTau.τ

Φ def

For a monic polynomial $p(x)=\prod_{i\le n}(x- \lambda_i)$, define $$\Phi_n(p):=\sum_{i\le n}(\sum_{j\neq i} \frac1{\lambda_i-\lambda_j})^2$$ and $\Phi_n(p):=\infty$ if $p$ has a multiple root. · Arxiv.«2602.05192».Φ

Φ def

The space Φ(G) of "convex combinations" of kernels from baseΦ. · Green57.Φ

φ def

def φ : ℝ · MovingSofa.GerversSofa.φ

Φ' def

The restricted space Φ′(G) of "convex combinations" of kernels from baseΦ'. · Green57.Φ'

χ def

The indicator function of a finset: χ s i = true ↔ i ∈ s. · DedekindNumber.χ

Ω def

For a real number α, define Ω(α) as $$ \Omega (\alpha )=\inf _{\theta > 0}\left({\limsup _{n\rightarrow \infty }\left\lbrace {\theta \alpha ^{n}}\right\rbrace -\liminf _{n\rightarrow \infty }\left\lbrace {\theta \alpha … · Mahler32.Ω

ω def

A convenient phase with squared norm $1/2$. Using $\omega = (1+i)/2$ avoids square roots. · OpenQuantumProblem13.Qubit.ω

ω def

The standard algebraic primitive cube root of unity. · OpenQuantumProblem23.ω

ℤAdjoinInvNat def

def ℤAdjoinInvNat (N : ℕ) : Subalgebra ℤ ℚ · LamLitt.ℤAdjoinInvNat

𝔽 abbrev

𝔽 p n is the vector space (Z/pZ)^n. When p is prime, this is $\mathbb{F}_p^n$. · 𝔽

𝔽₂ abbrev

𝔽₂ n is the vector space $\mathbb{F}_2^n$. · 𝔽₂

𝔽₃ abbrev

𝔽₃ n is the vector space $\mathbb{F}_3^n$. · 𝔽₃

𝔽₅ abbrev

𝔽₅ n is the vector space $\mathbb{F}_5^n$. · 𝔽₅

𝔽₇ abbrev

𝔽₇ n is the vector space $\mathbb{F}_7^n$. · 𝔽₇