有限向量空间的部分双线性函数构成的格 |
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作者姓名: | 齐艳芳 刘军丽 |
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作者单位: | 廊坊师范学院,河北廊坊065000 |
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基金项目: | 廊坊师范学院校级青年基金项目资助(LSZQ201304) |
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摘 要: | 设F(n)q为Fq上的n维向量空间,设P是由F(n)q上的所有m-部分双线性函数(V,f)和1构成的集合.在P上按照包含(或反包含)关系规定偏序,得到两类偏序,证明了这两类偏序集是有限格并计算了它们的M(o)bius函数和秩生成函数.
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关 键 词: | 双线性函数 向量空间 格 M(o)bius函数 秩生成函数 |
Lattices Associated with Partial Bilinear Functions of Finite Vector Spaces |
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Authors: | Qi Yan-Fang Liu Jun-li |
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Institution: | Qi Yan-Fang , Liu Jun-li |
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Abstract: | Let Fq^(n) denote the n-dimensional vector space over the finite field Fq, and let P be the set ot all m-partial bilinear functions ( V, f) of Fq(n) containing 1. Ordered P by ordinary and reverse inclusion, two families of finite posets are obtained. This paper proves that these pesets are lattices, and computes their Mobius functions and rank-generating functions. |
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Keywords: | bilinear function vector space lattice Msbius function rank-generating function |
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