Glossary: W

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

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W abbrev

An abbreviation for the van der Waerden number for 2 colors, commonly written as W(k). This represents the smallest integer N such that any 2-coloring of {1, ..., N} must contain a monochromatic arithmetic progression of length k. · Erdos138.W

W def

We define the 2-colour van der Waerden numbers $W(k, r)$ to be the least quantities such that if $\{1, ... , W(k, r)\}$ is coloured red and blue then there is either a red $k$-term progression or a blue $r$-term progression. · Green14.W

w def

w n counts the ordered quadruples $(a,b,c,d)$ of nonnegative integers with $n=2^a+3^b+2^c3^d$. · Erdos407.w

Weak def

The weak Birch and Swinnerton-Dyer conjecture for a number field $K$: for every elliptic curve $E$ over $K$, a meromorphic continuation of its $L$-series has order $\operatorname{rank}_{\mathbb{Z}} E(K)$ at $s = 1$. [Gross2011], … · BSD.Weak

WeaklyDivisible def

Say a set of natural numbers is k-weakly divisible if any k+1 elements of A are not relatively prime. · Erdos56.WeaklyDivisible

WeaklyFirstCountableTopology class

A topological space $X$ is called weakly first countable if there exists a function $N : X → ℕ → Set X$, such that: · WeaklyFirstCountable.WeaklyFirstCountableTopology

WeaklyNonTrilinear def

We say a subset A of points in the plane is weakly non-trilinear if it is a finite union of non-trilinear sets. · Erdos846.WeaklyNonTrilinear

weight def

The weight of an MZV index $(s_1, \ldots, s_k)$ is $s_1 + \cdots + s_k$. · ZagierMZV.weight

weighting def

The weighting $\vec{w}(t) = Z(t)^{-1}\mathbf{1}$ at scale t. · Arxiv.«2607.05349».weighting

WeightsN abbrev

Weights on edges. · MonochromaticQuantumGraph.WeightsN

weilArchimedean def

The additive Archimedean factor appearing in the Weil criterion. · RiemannHypothesis.weilArchimedean

weilNonArchimedean def

The additive non-Archimedean factor appearing in the Weil criterion. · RiemannHypothesis.weilNonArchimedean

WellSeparatedSet def

Let $A \subseteq (1, \infty)$ be a countably infinite set such that for all $x\neq y\in A$ and integers $k \geq 1$ we have $|kx - y| \geq 1$. · Erdos143.WellSeparatedSet

wheelSeven def

Wheel graph on 7 vertices (center + regular hexagon) with unit side length, touching both axes in the first quadrant. · Erdos91.wheelSeven

wichmannGaps def

The Wichmann ruler $W(r, s)$ [Wi63], given by its segment-length sequence $$1^r,\; (r+1),\; (2r+1)^r,\; (4r+3)^s,\; (2r+2)^{r+1},\; 1^r,$$ where $a^b$ denotes $b$ consecutive segments of length $a$. · SparseRuler.wichmannGaps

wienerIndex def

The Wiener index of G, which is the sum of distances between all pairs of vertices. · SimpleGraph.wienerIndex

windowThreshold def

The least window length y₀ such that every window (x, x+y) with y ≥ y₀ is ε-sparse, or ⊤ if no such y₀ exists. · Erdos450.windowThreshold

Witness4_d2 def

def Witness4_d2 : WeightsN 4 2 α · MonochromaticQuantumGraph.Witness4_d2

Witness4_d3 def

def Witness4_d3 : WeightsN 4 3 α · MonochromaticQuantumGraph.Witness4_d3

Witness6_d2 def

def Witness6_d2 : WeightsN 6 2 α · MonochromaticQuantumGraph.Witness6_d2

Word abbrev

Words are finite sequences of integers. · OeisA108081.Word

wordLength def

The word length of g with respect to the generating family P. · Group.Generators.wordLength

wordPrefix def

The prefix of a word w : Fin n → Fin q of length k + 1 (the first k + 1 characters). · SuffixPrefixAvoidance.wordPrefix

wordProd def

The canonical map from a word List (ι × Bool) over a generating family ι to its corresponding group G. · Group.Generators.wordProd

wordSuffix def

The suffix of a word w : Fin n → Fin q of length k + 1 (the last k + 1 characters). · SuffixPrefixAvoidance.wordSuffix

WormCovers def

The set of covers is the set of (measurable) sets that cover every worm by translation and rotation. · MoserWorm.WormCovers

Worms def

The set of worms is the set of curves of length (at most) 1. We formalize this as the set of ranges of 1-Lipschitz functions from [0,1] to ℝ². · MoserWorm.Worms

wowii103Counterexample abbrev

The 11-vertex counterexample: a triangle with four leaves on each of two vertices. · WrittenOnTheWallII.GraphConjecture103.wowii103Counterexample

wowii36Counterexample abbrev

A 10-vertex counterexample to Conjecture 36. · WrittenOnTheWallII.GraphConjecture36.wowii36Counterexample