| 王毅.一类子空间格(英文)[J].数学研究及应用,1999,19(2):341~348 |
| 一类子空间格(英文) |
| On a Class of Subspace Lattices |
| 投稿时间：1997-02-23 |
| DOI：10.3770/j.issn:1000-341X.1999.02.005 |
| 中文关键词: |
| 英文关键词:poset subspace lattice Sperner property q analog. |
| 基金项目: |
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| 摘要点击次数: 2117 |
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| 中文摘要: |
| 令Ｖn（ｑ）是具ｑ个元素的有限域上的ｎ维向量空间．Ｃ［ｎ，ｋ］是Ｖn（ｑ）中与某ｋ维子空间相交不为零空间之子空间全体按包含关系所成偏序集，Ｗm为其Ｗｈｉｔｎｅｙ数（０≤ｍ≤ｎ）．本文证明了Ｃ［ｎ，ｋ］具Ｓｐｅｒｎｅｒ性质和单峰性质．进一步地，Wm2-qWm-1Wm+1作为ｑ的多项式具有非负系数，并且W0≤Wn≤W1≤Wn-1≤W2≤…． |
| 英文摘要: |
| Let Vn(q) be the n-dimensional vector space over the finite field with q elements and Ln(q) denote the lattice of subspaces of Vn(q). Let , K a k-dimensional subspace and C[n,k] the set of the subspaces S such that S∩K≠=O. We show that C[n,k] is Sperner and unimodal and point out all maximum-sized antichains in C[n,k]. For the Whitney number Wm of C[n,k], we show that Wm2-qWm-1Wm+1 has nonnegative coefficients as a polynomial in q and that W0≤Wn≤W1≤Wn-1≤W2≤…. |
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