Some Conjectures for Immanants
Some Conjectures for Immanants
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关于内在体的一些猜想
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发表时间：
1992
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通讯作者：
J. Stembridge
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作者：
J. Stembridge
我们提出了一系列关于内在的猜想，以及我们所拥有的支持证据。这些猜想大致可分为三类。第一类是关于全正矩阵内嵌式的不等式。，具有非负子式的实矩阵)。这包括，例如，全正矩阵的内变量是非负的猜想。第二族涉及Jacobi-Trudi矩阵的内嵌项。这些猜想是由Goulden和Jackson先前的猜想（最近由C. Greene证明）提出的，即Jacobi-Trudi矩阵的内变量是具有非负系数的多项式。第三类涉及与无环有向图中的总正性和路径相关的几何和组合结构。
Abstract We present a series of conjectures for immanants, together with the supporting evidence we possess for them. The conjectures are loosely organized into three families. The first concerns inequalities involving the immanants of totally positive matrices (Le.,real matrices with nonnegative minors). This includes, for example, the conjecture that immanants of totally positive matrices are nonnegative. The second family involves the immanants of Jacobi-Trudi matrices. These conjectures were suggested by a previous conjecture of Goulden and Jackson (recently proved by C. Greene) that the immanants of Jacobi-Trudi matrices are polynomials with nonnegative coefficients. The third family involves geometric and combinatorial structures associated with total positivity and paths in acyclic digraphs.