线性格中t-交反链的LYM-型不等式

LYM-type inequality for t-intersecting antichains in linear lattices

线性格Ln(q)是q元域上n维线性空间的所有子空间组成的格.两个子空间称为t-交的,如果它们交空间的维数不小于t.已知线性格的1-交反链满足LYM(Lubell-Yamamoto-Meschalkin)-型不等式,本文讨论线性格中t-交反链的LYM-型不等式,并在一些特殊情形下证明该不等式.

The linear lattice Ln（q） is the lattice of subspaces of the n-dimensional vector space over the field of q elements. Two subspaces are called t-intersecting if the dimension of their intersection is greater than or equal to t. It is well known that 1-intersecting antichains in Ln（q） satisfy LYM-type inequality. In this paper, we discuss the LYM-type inequality for t-intersecting antichains, and establish it in some special cases.