Inequalities for two systems of subspaces with prescribed intersections

TL;DR

This paper introduces bounds on the size of specific systems of subspaces within a linear space, focusing on weak ISP and (u,v)-systems with prescribed intersections.

Contribution

It defines weak ISP and (u,v)-systems of subspaces and establishes upper bounds for their sizes, advancing understanding of subspace intersection properties.

Findings

Upper bounds for weak ISP-systems

Upper bounds for weak (u,v)-systems

Framework for analyzing subspace intersection inequalities

Abstract

Let $W$ denote a linear space over a fixed field ${\mathbb F}$. We define the notions of weak $ISP$-system and weak $(u,v)$-system $\cal S=\{(U_i,V_i):~ 1\leq i\leq m\}$ of subspaces of $W$. We give upper bounds for the size of weak $ISP$-systems and weak $(u,v)$-systems.