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We refer to the vector $(a_0(A),\ldots,a_n(A))$ as the \emph{statistics} of $A$. We define the $i \item A vector $(a_0,\ldots,a_n)$ of non-negative integers is \emph{feasible} if it is the ...

...scriptstyle {\mathbf x}</math> be a <math> \scriptstyle \pm1</math> column vector (our coloring!), and let <math>\delta</math> be the maximum discrepancy of * Let <math>P_i</math> be the indicator vector of the <math>i</math>-th AP. Suppose that we have some <math>\lambda_{i,j}< ...

\begin{definition} Given a vector $\slice \in \N^k$ whose components sum to $n$, the associated \emph{slice} ...ividing it into arcs, the associated \emph{spacing} is the $k$-dimensional vector $\spac$ defined by setting $\spac[a]$ to be the length of the arc emanating ...

{ // initialize divisors table (s), lengths vector (l) and is_prime vector { // initialize coordinates vector (x) ...

...ncy result to vector-valued functions. More precisely, if each $f(x)$ is a vector in some Euclidean space $H$, then we have the lower bound ...e as well: if $\disc_\A(f)$ is at least $t$ whenever each $f(x)$ is a unit vector in some Hilbert space $H$, then we can find coefficients $\lambda_A$ and $b ...

...\dots,B_n</math> are <math>n</math> bases of an <math>n</math>-dimensional vector space <math>V</math> (not necessarily distinct or disjoint), then there exi ...0 in a field <math>F</math>, then RBC holds for <math>n</math>-dimensional vector spaces over <math>F</math>. ...

...interpretation of the heat equation. But one can also establish it via a vector-valued maximum principle argument, as follows. At the initial time zero, w ...ite up the graph G_n has 2^n rows so if you wanted to simulate the Fiedler vector for G_6 with edge weights a=1,b=2,c=3 then you would type HotSpotsAny(64,1, ...

Let <math>\omega := \exp( i \pi/3)</math> be the sixth root of vector, then we have the identities ...\frac{i}{2} \arccos(\frac{5}{6})),</math> then <math>\eta</math> is a unit vector that obeys the identity ...

...e nature of this equation will determine whether we need a real or complex vector space to describe the set of all possible quantum voter states. Thus far, w ...</math> is the projection onto the <math>i</math> coordinate of the random vector <math>X</math> ...

...ivation of Hilbert-space EDP from (*) follows the argument above (f is now vector-valued instead of scalar, but Plancherel's theorem and all the other tools ...

% There is assumed a vector of 27-bit DISALLOWED numbers in DVEC % There is assumed a vector of 27-bit DISALLOWED numbers in DVEC ...

Let’s say that a vector in <math>\mathbb{F}_3^r</math> is simple if either 1, or 2 does not appear ...

...ices to check that density function <math>f(w_1, \dots, w_k)</math> of the vector <math>\vec{W}</math> depends only on <math>w_1 + \cdots + w_k</math>. Now < ...

...(In general, they show that a Kakeya set in the <math>n</math>-dimensional vector space over the <math>q</math>-element field has at least <math>(q/(2-1/q))^ ...

where $c$ is the $k-1$-dimensional vector, all of whose entries are equal to $\lfloor n/k \rfloor$. ...

...f the same size and the same sum. Hence, if we replace the letter i by the vector (1,i), we get a path in Z^2 that does not contain arithmetic progressions o ...

...ce. It prints the list of integers n such that {n, 2n, 3n, ...} is a basis vector to stdout. ...

#include <vector> std::vector<int> v_; ...

...de <math>\Omega_A</math>, and whose Hessian maps the outward normal n to a vector with radial component <math>c_{AB}</math> on AB and <math>c_{AC}</math> on ...

...e formed by a set of vectors <math>V</math> of unit length. Often a single vector is used many times in the same graph for different edges. The vectors gener ...