Glossary: T

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

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T def

For a finite sequence of $n$ (not necessarily distinct) integers $A = (x_1,\ldots,x_n)$, the sequence T a b A of length $rn$ given by $(a_ix_j+b_i)_{1\leq j\leq n, 1\leq i\leq r}$. · Erdos481.T

T def

T n r is maximal such that there exists a family $\mathcal{F}$ of subsets of $\{1,\ldots,n\}$ of size T n r such that $\lvert A\cap B\rvert\neq r$ for all $A,B\in \mathcal{F}$ (including $A=B$). · Erdos703.T

T def

The maximum number of transversals over all latin squares of order n. · LatinSquare.T

T def

T n k is the array defined as $T(1,1) = 1$, $T(i,j) = 0$ if $i<1$ or $j<1$, $T(n,k) = T(n,k-2) + T(n,k-1) - 2 T(n-1,k-1) + T(n-1,k) + T(n-2,k)$. · OeisA112521.T

t def

t φ is the Boxdot translation of a formula φ. Roughly, t is the mapping φ ↦ t φ from the language of monomodal logic into itself that preserves variables and the logical constant ⊥, commutes with the standard truth-functional … · Arxiv.«1308.0994».t

t def

t_x such that u_0 ... u_{t_x-1} ≤ x < u_0 ... u_{t_x}. · Erdos1101.t

t def

t n is the largest t such that n! is a product of n factors all at least t, i.e. the maximal $a_1$ in a representation $n! = a_1 \cdots a_n$ with $a_1 \leq \cdots \leq a_n$. · Erdos391.t

t def

Let $t_k(n)$ denote the least $m$ such that $n\mid m(m+1)(m+2)\cdots (m+k-1).$ · Erdos394.t

t def

The minimum number of points in $\{1,\ldots,n\}^2$ such that the lines determined by these points cover all points in $\{1,\ldots,n\}^2$. · Erdos798.t

t def

t n is the least T such that {n + 1, …, n + T} contains a subset whose product with n is a square; t n = 0 if and only if n is itself a square. · Erdos841.t

t def

t n is used in the second conjecture. · OeisA114362.t

tamagawaNumber def

The local Tamagawa number attached to an integral model. For a minimal model this is the usual Tamagawa number. This is 0 if there are infinitely many distinct translates. · WeierstrassCurve.Projective.tamagawaNumber

tamagawaProduct def

The product of local Tamagawa numbers for minimal integral models at all the non-archimedean completions. This is 1 if infinitely many local factors differ from 1. · WeierstrassCurve.Projective.tamagawaProduct

TAnySize def

Maximum number of equilateral triangles of any size spanned by $n$ points in $\mathbb{R}^d$. · Erdos755.TAnySize

tateShafarevich def

The Tate–Shafarevich group of a Galois module. · ContinuousCohomology.tateShafarevich

tateShafarevich def

The subgroup of the first continuous Galois cohomology group consisting of classes whose restrictions vanish at every infinite and finite place. When W.IsElliptic, this is the classical Tate--Shafarevich group of W over K. The … · WeierstrassCurve.Affine.tateShafarevich

tauPlus def

tauPlus n (written $\tau^+(n)$) counts the number of $k$ such that $n$ has a divisor in $[2^k, 2^{k+1})$. Equivalently, the number of distinct values $\lfloor \log_2 d \rfloor$ as $d$ ranges over the divisors of $n$: a divisor $d$ lies … · Erdos448.tauPlus

temp_v def

temp_v G v = deg(v)/(n(G) - deg(v)). · SimpleGraph.temp_v

term def

$k^{\mu(k)}$ as a rational number. · OeisA80326.term

terms def

The terms of the sequence of Erdős Problem 430 for a given $n$: the integers $m$ with $1 < m < n$ all of whose prime factors are $> n - m$. · Erdos430.terms

test_def def

def test_def : Nat · Foo.test_def

test_def_no_namespace def

def test_def_no_namespace : Nat · test_def_no_namespace

tetraA def

The first real amplitude used in the tetrahedral qubit SIC. · OpenQuantumProblem23.tetraA

tetraB def

The second real amplitude used in the tetrahedral qubit SIC. · OpenQuantumProblem23.tetraB

tetrahedral def

The $n$-th tetrahedral number: $T_n = \frac{n(n+1)(n+2)}{6}$. · PollocksConjecture.tetrahedral

tilesByTranslation def

A set Ω tiles ℝ^d by translation if there exists a set T of translation vectors such that the translates of Ω by T cover ℝ^d without overlap. · tilesByTranslation

Tn def

The map $T_n$ sends $x$ to $nx \bmod 1$ on the additive circle. · Arxiv.id2303_01089.Tn

toAMS def

Checks if a command has the AMS attribute. · AMSLinter.toAMS

toCategories def

Extract the categories from a declaration's modifiers. · ProblemAttributes.toCategories

toCategory def

Checks if a command has the category attribute. · CategoryLinter.toCategory

toCategory def

Convert from a syntax node to a term of type Category and annotate the syntax with the corresponding name's docstring. · ProblemAttributes.Syntax.toCategory

toCategorySyntax def

Extract the category attributes from a declaration's modifiers. · ProblemAttributes.toCategorySyntax

toDirSyntax def

Char.toDirSyntax c outputs the syntax corresponding to the character c if c is R or L and throws an error in other cases. This is used when parsing the "direction" component of turing machine string representations. · Char.toDirSyntax

toDualNumber def

The map to the dual numbers (ℤ/ℓ)[ε] attached to a homomorphism φ : Fˣ → ℤ/ℓ: it sends {a} to φ(a) ε and kills every product of two classes of degree one, so in particular it kills the Steinberg relations. · MilnorK.toDualNumber

toHypergraph def

The hypergraph with edge family H and ground vertex set S. · Finset.toHypergraph

toIdeal def

A right ideal in a commutative semiring, regarded as an ideal. · RightIdeal.toIdeal

toModule def

def VectorBundles.toModule : S.VectorBundles ⥤ S.Modules · AlgebraicGeometry.Scheme.VectorBundles.toModule

toName def

def formalProofKind.toName (stx : TSyntax ``formalProofKind) : Option Name · ProblemAttributes.formalProofKind.toName

toName def

Convert from a syntax node to a name. · ProblemAttributes.problemStatus.toName

toNat? def

def AMS.toNat? (a : AMS) : Option Nat · AMS.toNat?

toNumeralSyntax def

Char.toBinarySyntax c outputs the syntax corresponding to the character c if c is in 0, ..., 9 and throws an error in other cases. This is used when parsing the "symbol" component of turing machine string representations. · Char.toNumeralSyntax

toRightIdeal def

An ideal in a commutative semiring, regarded as a right ideal. · RightIdeal._root_.Ideal.toRightIdeal

TorontoSpace class

A Toronto space is a topological space which is homeomorphic to all of its subspaces of same cardinality. · Toronto.TorontoSpace

toSet def

Converts a rectangle to a set in ℝ × ℝ. · Mathoverflow34145.Rectangle.toSet

toSimpleGraph def

The simple graph of a Young diagram: two distinct cells are adjacent iff they lie in the same row or in the same column. · YoungDiagram.toSimpleGraph

toSperner def

Forward map: monotone function → Sperner family (the minimal true sets). · DedekindNumber.toSperner

toStateName def

The name of the state type with n constructors A, B, .... · Nat.toStateName

toStateSyntax def

Char.toStateSyntax c stateName outputs the syntax of the constructor corresponding to c if c is a capital letter (i.e. something between A and Z.). For example, A would output the syntax stateName.A where stateName is the … · Char.toStateSyntax

toStateSyntax def

Nat.toStateSyntax n stateName outputs the syntax of the n-th constructor of the type used to index states. · Nat.toStateSyntax

toStmtSyntax def

String.toStmtSyntax s stateName parses a component of a Turing machine string representation and outputs the syntax of the corresponding (state, statement) : State × Stmt pair. · String.toStmtSyntax

toSubjects def

Converts a syntax node to an array of AMS subjects. · ProblemAttributes.Syntax.toSubjects

totalDominationNumber def

The total domination number of G. · SimpleGraph.totalDominationNumber

totalLength def

The total length of a family of cycles. · Arxiv.«2607.06396».totalLength

Tournamenton structure

A tournamenton is a measurable function W : [0, 1] × [0, 1] → [0, 1] satisfying the tournament condition W(x, y) + W(y, x) = 1. · LimitObjects.Tournamenton

tournamentonHomDensity def

The homomorphism density $t_{\vec{T}}(W)$ of a digraph $D$ in a tournamenton $W$ on $[0, 1]$ equipped with the Lebesgue measure volume. · LimitObjects.tournamentonHomDensity

tournamentonHomIntegrand def

The integrand for the homomorphism density $t_{\vec{T}}(W)$ of a digraph $D$ in a tournamenton $W$ given a configuration x : V → [0, 1]. · LimitObjects.tournamentonHomIntegrand

toWeierstrass def

Convert the structure RatEllipticCurve to a Weierstrass curve. · EllipticCurveRank.RatEllipticCurve.toWeierstrass

transformed_shadow def

The result of transforming a subset of ℝ³ by a chosen rotation and offset, and then projected to ℝ². · Rupert.transformed_shadow

translateSet def

The translate of a set Ω by a vector t. · translateSet

triangle_area def

def triangle_area (a b c : P) : ℝ · EuclideanGeometry.triangle_area

triangleFreeMaxChromatic def

Maximum chromatic number of a triangle-free graph on n vertices. · Erdos1104.triangleFreeMaxChromatic

trianglesContaining def

The triangles of G containing the edge uv, that is, the 3-cliques of G whose vertex set contains both endpoints of uv. · SimpleGraph.trianglesContaining

triangular def

The $n$-th triangular number. · OeisA100474.triangular

triangular def

The $n$-th triangular number, $T_n = \frac{n(n+1)}{2}$. · OeisA53067.triangular

triangularNumber def

Triangular number $T_c = c(c+1)/2$. · OeisA105020.triangularNumber

tribonacci def

The Tribonacci numbers $T_n$ (A000073). $T_0=0, T_1=0, T_2=1$, and $T_n = T_{n-1} + T_{n-2} + T_{n-3}$ for $n \ge 3$. · OeisA271591.tribonacci

trigPoly def

The trigonometric polynomial $f(z) = \sum_{0\leq k\leq n}c_k e^{ikz}$, as an entire function of $z\in\mathbb{C}$. · Erdos225.trigPoly

trinaryLists def

Lists of length k with entries in {-1, 0, 1}. · OeisA109074.trinaryLists

tripleKernel def

Uniform average over pairs (x₁, x₂) in G × G, with the third variable determined by the relation x₁ + x₂ + x₃ = g. The functions fᵢ are complex-valued. · Green57.tripleKernel

tripleProduct def

We define the product of two triples $(a, b, c)$ and $(d, e, f)$ by $((a, d), (b, e), (c, f))$, where the pairs are ordered lexicographically. · Arxiv.«1609.08688».tripleProduct

tripleRep def

The number of representations of n as an ordered sum of three elements of A, $1_A\ast 1_A\ast 1_A(n)$. · Erdos764.tripleRep

Triplewise def

The ternary relation r holds triplewise on the set s if r x y z for all distinct x y z ∈ s. · Set.Triplewise

Triplewise def

def Triplewise {α : Type*} (r : α → α → α → Prop) : Prop · Triplewise

trivialModuleCat def

The trivial module of the bialgebra A over R: the ring R on which A acts through the counit A →ₐ[R] R, as an object of ModuleCat A. · Bialgebra.trivialModuleCat

trivialModuleCatLinearEquiv def

The trivial module of a bialgebra over a field k is k itself as a k-module; in particular it is one-dimensional. · Bialgebra.trivialModuleCatLinearEquiv

TrivialRuler abbrev

The trivial ruler with all marks $\{0, \dots, N\}$. · Erdos170.TrivialRuler

trivialZeros def

Let $\chi$ be a Dirichlet character, trivialZeros is the set of trivial zeros of the Dirichlet $L$-function of $\chi$ which is always a set of non-positive integers. - $\chi = 1$ then the Dirichlet $L$-function is the Riemann zeta … · GRH.trivialZeros

truncatedExp def

The truncated exponential polynomial truncatedExp n is given by ∑_{j=0}^{n} x^j / j! over ℚ, which is the n-th partial sum of the Taylor series for the exponential function e^x. · SchurTruncatedExponential.truncatedExp

TUnit def

Maximum number of unit equilateral triangles spanned by $n$ points in $\mathbb{R}^d$. · Erdos755.TUnit

turanNumber abbrev

The number of edges of the Turán graph $T(n, r)$, i.e. the Turán number. · Erdos904.turanNumber

twistIndexLE def

The set of nonzero integers $d$ with $|d| \leq H$, which index the quadratic twists $E^d$ ordered by $|d|$. By naiveHeight_quadraticTwist this is the same as ordering them by height. · EllipticCurveRank.RatEllipticCurve.twistIndexLE

twistRank abbrev

The rank of the quadratic twist $E^d$ of an elliptic curve $E$ over $\mathbb{Q}$. · EllipticCurveRank.RatEllipticCurve.twistRank

twoPowAddPrimeSet def

The set of integers of the form 2^k+p, where k ≥ 0 and p is prime. · Erdos851.twoPowAddPrimeSet

TwoPowAddSet def

TwoPowAddSet r is the set of integers of the form 2^k+n, where k ≥ 0 and n has at most r prime divisors. · Erdos851.TwoPowAddSet