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Combinatorial Aspects of Total Weight Orders over Monomials of Fixed Degree

机译：固定度单项式上的总权重顺序的组合方面

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Among all the restrictions of weight orders to the subsets of monomials with a fixed degree, we consider those that yield a total order. Furthermore, we assume that each weight vector consists of an increasing tuple of weights. Every restriction, which is shown to be achieved by some monomial order, is interpreted as a suitable linearization of the poset arising by the intersection of all the weight orders. In the case of three variables, an enumeration is provided. For a higher number of variables, we show a necessary condition for obtaining such restrictions, using deducibility rules applied to homogeneous inequalities. The logarithmic version of this approach is deeply related to classical results of Farkas type, on systems of linear inequalities. Finally, we analyze the linearizations determined by sequences of prime numbers and provide some connections with topics in arithmetic.
机译：在对具有固定度的单项式子集的权重顺序的所有限制中，我们考虑那些产生总顺序的限制。此外，我们假设每个权重向量都由一个递增的权重元组组成。被证明是通过某个单项阶数实现的每个限制，都被解释为由所有权重阶数的相交产生的合适的波状体线性化。在三个变量的情况下，提供了一个枚举。对于更多数量的变量，我们使用适用于齐次不等式的演绎规则，显示了获得此类限制的必要条件。这种方法的对数形式与线性不等式系统上的Farkas型经典结果密切相关。最后，我们分析质数序列确定的线性化，并在算术上提供与主题的联系。

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