论文标题
分区身份和应用于无限尺寸的groebner和Viceversa
Partition identities and application to infinite dimensional Groebner basis and viceversa
论文作者
论文摘要
在本文的第一部分中，我们考虑了“加权词典单一秩序”的差异理想{x_1^2}的差异基础，并表明其计算与涉及第一个Rogers-Ramanujan身份的分区的身份相关。然后，我们证明，与“加权反向词典”的情况相反，这种理想的基础并非有限。在第二部分中，我们给出了nguyen duc tam定理的简单而直接的证明，内容涉及差异理想的gro依基础{x_1y_1};然后，我们获得涉及2种颜色的分区的身份。
In the first part of this article, we consider a Groebner basis of the differential ideal {x_1^2} with respect to "the" weighted lexicographical monomial order and show that its computation is related with an identity involving the partitions that appear in the first Rogers-Ramanujan identity. We then prove that a Grobener basis of this ideal is not differentially finite in contrary with the case of "the" weighted reverse lexicographical order. In the second part, we give a simple and direct proof of a theorem of Nguyen Duc Tam about the Groaner basis of the differential ideal {x_1y_1}; we then obtain identities involving partitions with 2 colors.
