Glossary: K

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

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k def

The curling number · Arxiv.«0912.2382».k

k def

The largest integer k such that any unit-distance-avoiding colouring contains a congruent red copy of every set of k points. · Erdos214.k

k abbrev

Let $k(N)$ denote the smallest $k$ such that there exists $N ≤ n_1 < ⋯ < n_k$ with $\frac 1 {n_1} + ... + \frac 1 {n_k} = 1$. · Erdos295.k

k def

The 2-adic valuation of $n(n+1)$. · Erdos933.k

k def

Let $k(n)$ be the maximal $k$ such that there exists $m \le n$ with $m+1, \ldots, m+k$ each divisible by a prime $> k$. · Erdos962.k

K133 abbrev

The complete tripartite graph $K_{1,3,3}$. · Erdos1007.K133

K33 def

$K_{3,3}$ is the complete bipartite graph with partition sizes 3, 3 (6 vertices, 9 edges). · Erdos567.K33

K4 abbrev

K4: Complete graph on 4 vertices. · WrittenOnTheWallII.Test.K4

KacCoefficients structure

A sequence of Kac coefficients over a subset S of a field k is a countably infinite sequence of independent random variables, each uniformly distributed over S with respect to the reference measure μ. The default reference … · Erdos522.KacCoefficients

KakeyaSetConjectureDim def

The Kakeya set conjecture in dimension n: the statement that every Kakeya set in ℝⁿ has Hausdorff dimension n. · Kakeya.KakeyaSetConjectureDim

kernel def

The squarefree kernel $K_n$ of $\omega_n$: the product of the primes dividing it to an odd power, so 1 when there are none. · Arxiv.«2607.05739».kernel

kisielewiczFormula def

A closed formula for the Dedekind numbers as found by Kisielewicz (1998): $$ M(n) = \sum_{k=0}^{2^{2^n}}\prod_{j = 1}^{2 ^ n - 1}\prod_{i = 0}^{j - 1} \left( 1 - b_i^kb_j^k \prod_{m = 0}^{\log_2 i} (1 - b_m^i + b_m^ib_m^j)\right), $$, … · DedekindNumber.kisielewiczFormula

kKernel def

The k-kernel of a sequence a is the set of subsequences $(a_{k^e n + r})_{n \ge 0}$ with $e \ge 0$ and $0 \le r < k^e$. · AutomaticSequence.kKernel

knownIdonealNumbers def

The 65 known idoneal numbers that are conjectured to be the only idoneal numbers. · Idoneal.knownIdonealNumbers

knPlusTEdges def

The graph formed by connecting a new vertex (none) to $t$ of the vertices of $K_n$ (Fin n). · Erdos545.knPlusTEdges

KotheRadical def

The Kothe Radical of a ring R is the sum of all (two-sided) nil ideals of R. Tags: Kothe Radical, upper nilradical · Koethe.KotheRadical

KProof inductive

KProof Γ φ is the usual Hilbert‐style proof relation for the minimal normal modal logic K, with assumptions drawn from Γ. · Arxiv.«1308.0994».KProof

KT def

KT is the specific normal modal logic whose theorems are exactly those provable in KTProof from the empty context. · Arxiv.«1308.0994».KT

kthPrimeFactor def

The $k$-th smallest distinct prime factor of an integer $n$ (where $k \ge 1$). This is defined as the $k$-th element (0-indexed $k-1$) of the increasing list of distinct prime factors of n.natAbs. Returns 1 if n has fewer than k distinct … · OeisA382590.kthPrimeFactor

kthPrimeFactorSet def

The set of positive integers whose k-th smallest prime factor is p: if $p_1<p_2<\cdots$ are the primes dividing $n$ then $p_k=p$. · Erdos690.kthPrimeFactorSet

KTProof inductive

KTProof Γ φ denotes that φ is provable from the premises Γ in the normal modal logic KT (also called T). KT extends system K by adding the instances of the T-axiom schema □φ ~> φ to K’s usual axioms and rules of inference. · Arxiv.«1308.0994».KTProof