Glossary: V

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

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V abbrev

Let V(x) count the number of n≤x such that ϕ(m)=n is solvable. · Erdos416.V

V def

$V(n,k)$ is the number of primes $p$ such that $p^\alpha$ exactly divides $n+k$ and for all $0 \le i < k$, $p^\alpha$ does not divide $n+i$, where $\alpha$ is the multiplicity of $p$ in the factorization of $n+k$. · Erdos889.V

V def

The Lucas sequence of the second kind $V_0(P, Q) = 0$, $V_1(P, Q)=P$, $V_{n+2}(P, Q)=PV_{n+1}(P, Q)-QV_n(P, Q)$ · LucasSequence.V

V abbrev

Vertices of $K_N$. · MonochromaticQuantumGraph.V

v def

$v(n,k)$ counts the prime factors of $n+k$ which do not divide $n+i$ for all $0 \le i < k$. · Erdos889.v

V_l def

$V_l(n)$ is the supremum of $V(n,k)$ for all $k \ge l$ · Erdos889.V_l

v_l def

$v_l(n)$ is the supremum of $v(n,k)$ for all $k \ge l$ · Erdos889.v_l

Valid def

A vertex of the strengthened problem: a visible lattice point with both coordinates exceeding 1 and at least one coordinate composite. · Erdos1212.Valid

ValidCardinalities def

The set of cardinalities of all subsets A where A - A intersects {-1, 0, 1}^n only at 0. · Green38.ValidCardinalities

ValidClass def

The modulus is > 1 and the residue is reduced. · Erdos1188.ValidClass

ValidExponent def

True if the given exponent satisfies Green's conditions [Gr26]. · Green19.ValidExponent

value def

Public API: The game-theoretic value of Catch-Up on the set S, assuming optimal play. Returns .win if player 1 wins, .loss if player 2 wins, .draw if the game is tied. · CatchUp.value

valueAux def

value remaining s_me s_opp isFirstMove evaluates the position where: · CatchUp.valueAux

Vars abbrev

abbrev Vars · OeisA2897.Vars

vec2 def

A convenient constructor for qubit state vectors. · OpenQuantumProblem23.vec2

vec3 def

A convenient constructor for qutrit state vectors. · OpenQuantumProblem23.vec3

vecOfList def

The vector in ℤ^d whose i-th coordinate is the i-th entry of the list l, or 0 if l has fewer than i + 1 entries. Used to encode the inputs of the reachability problem. · BranchingVAS.vecOfList

VectorBundleData structure

A vector bundle is a sheaf of modules that is locally isomorphic to a free sheaf. · SheafOfModules.VectorBundleData

VectorBundles structure

A vector bundle over a scheme S is a locally free $\mathcal{O}_S$-module of finite rank. · AlgebraicGeometry.Scheme.VectorBundles

verifyCategoryCounts def

Verify that the list of problems contains the expected number of problems for each category. Throws an error if counts do not match. · ProblemAttributes.verifyCategoryCounts

Vertex abbrev

The vertex type: vectors in (ZMod m)³. · ClaudesCycles.Vertex

verticalHallway def

The vertical side of the hallway is $[0, 1] \times (-\infty, 1]$. · MovingSofa.verticalHallway

vertices def

Ordered vertex list $[0, 1, \ldots, N-1]$. · MonochromaticQuantumGraph.vertices

visitAverage def

The proportion $\frac{1}{n}\sum_{1\leq k\leq n}1_{\{k\alpha \}\in E}$ of the fractional parts $\{k\alpha\}$, $1\leq k\leq n$, which lie in E. · Erdos994.visitAverage

visitStateOf def

Visit nodes in an infotree, where state is set only within a single branch. · Lean.Elab.InfoTree.visitStateOf

v₀ def

$v_0(n)$ is the supremum of $v(n,k)$ for all $k \ge 0$. · Erdos889.v₀