ترغب بنشر مسار تعليمي؟ اضغط هنا

On k-caps in PG(n, q), with q even and n geq 4

159   0   0.0 ( 0 )
 نشر من قبل Joseph A. Thas
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Joseph A. Thas




اسأل ChatGPT حول البحث

Let $m_2(n, q), n geq 3$, be the maximum size of k for which there exists a complete k-cap in PG(n, q). In this paper the known bounds for $m_2(n, q), n geq 4$, q even and $q geq 2048$, will be considerably improved.



قيم البحث

اقرأ أيضاً

76 - Michael Tait , Robert Won 2020
An $m$-general set in $AG(n,q)$ is a set of points such that any subset of size $m$ is in general position. A $3$-general set is often called a capset. In this paper, we study the maximum size of an $m$-general set in $AG(n,q)$, significantly improvi ng previous results. When $m=4$ and $q=2$ we give a precise estimate, solving a problem raised by Bennett.
We consider tree level form factors of operators from stress tensor operator supermultiplet with light-like operator momentum $q^2=0$. We present a conjecture for the Grassmannian integral representation both for these tree level form factors as well as for leading singularities of their loop counterparts. The presented conjecture was successfully checked by reproducing several known answers in $mbox{MHV}$ and $mbox{N}^{k-2}mbox{MHV}$, $kgeq3$ sectors together with appropriate soft limits. We also discuss the cancellation of spurious poles and relations between different BCFW representations for such form factors on simple examples.
For each natural number $d$, we introduce the concept of a $d$-cap in $mathbb{F}_3^n$. A subset of $mathbb{F}_3^n$ is called a $d$-cap if, for each $k = 1, 2, dots, d$, no $k+2$ of the points lie on a $k$-dimensional flat. This generalizes the notion of a cap in $mathbb{F}_3^n$. We prove that the $2$-caps in $mathbb{F}_3^n$ are exactly the Sidon sets in $mathbb{F}_3^n$ and study the problem of determining the size of the largest $2$-cap in $mathbb{F}_3^n$.
230 - Xuezhang Chen 2015
In this paper, we employ a nonlocal $Q$-curvature flow inspired by Gursky-Malchiodis work cite{gur_mal} to solve the prescribed $Q$-curvature problem on a class of closed manifolds: For $n geq 5$, let $(M^n,g_0)$ be a smooth closed manifold, which is not conformally diffeomorphic to the standard sphere, satisfying either Gursky-Malchiodis semipositivity hypotheses: scalar curvature $R_{g_0}>0$ and $Q_{g_0} geq 0$ not identically zero or Hang-Yangs: Yamabe constant $Y(g_0)>0$, Paneitz-Sobolev constant $q(g_0)>0$ and $Q_{g_0} geq 0$ not identically zero. Let $f$ be a smooth positive function on $M^n$ and $x_0$ be some maximum point of $f$. Suppose either (a) $n=5,6,7$ or $(M^n,g_0)$ is locally conformally flat; or (b) $n geq 8$, Weyl tensor at $x_0$ is nonzero. In addition, assume all partial derivatives of $f$ vanish at $x_0$ up to order $n-4$, then there exists a conformal metric $g$ of $g_0$ with its $Q$-curvature $Q_g$ equal to $f$. This result generalizes Escobar-Schoens work [Invent. Math. 1986] on prescribed scalar curvature problem on any locally conformally flat manifolds of positive scalar curvature.
A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. In this paper, we describe a deformation of this correspondence for $SL(N)$. We introduce a difference equation version of opers called $q$-opers and prove a $q$-Langlands correspondence between nondegenerate solutions of the Bethe ansatz equations for the XXZ model and nondegenerate twisted $q$-opers with regular singularities on the projective line. We show that the quantum/classical duality between the XXZ spin chain and the trigonometric Ruijsenaars-Schneider model may be viewed as a special case of the $q$-Langlands correspondence. We also describe an application of $q$-opers to the equivariant quantum $K$-theory of the cotangent bundles to partial flag varieties.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا