论文标题
交叉$ t $ - 建立符号极性空间的家庭
Cross $t$-intersecting families for symplectic polar spaces
论文作者
论文摘要
令$ \ mathscr {p} $为有限字段$ \ mathbb {f} _q $和$ \ mathscr {p} _m $表示所有$ k $ diperimential-dipermential-Dipermential-Dipertropic suppace in $ \ m m iathscr {p} $。令$ \ mathscr {f} _1 \ subset \ mathscr {p} _ {m_1} $和$ \ Mathscr {f} _2 \ subset \ subset \ mathscr {p} _ {m_2} _ {m_2} $ $ f_1 \ in \ mathscr {f} _1 $和$ f_2 \ in \ mathscr {f} _2 $。我们说他们是交叉的$ t $ quistectrate家庭。此外，我们说，如果每个成员都包含固定的$ t $ dimensional完全同型子空间，那么它们是微不足道的。在本文中，我们表明，具有最大尺寸产物的交叉$ T $更换家庭是微不足道的。我们还描述了具有最大尺寸产物的非平凡$ t $更换家庭的结构。
Let $\mathscr{P}$ be a symplectic polar space over a finite field $\mathbb{F}_q$, and $\mathscr{P}_m$ denote the collection of all $k$-dimensional totally isotropic subspace in $\mathscr{P}$. Let $\mathscr{F}_1\subset\mathscr{P}_{m_1}$ and $\mathscr{F}_2\subset\mathscr{P}_{m_2}$ satisfy $\dim(F_1\cap F_2)\ge t$ for any $F_1\in\mathscr{F}_1$ and $F_2\in\mathscr{F}_2$. We say they are cross $t$-intersecting families. Moreover, we say they are trivial if each member of them contains a fixed $t$-dimensional totally isotropic subspace. In this paper, we show that cross $t$-intersecting families with maximum product of sizes are trivial. We also describe the structure of non-trivial $t$-intersecting families with maximum product of sizes.
