论文标题
随机排序多面体和流程多型的邻接
Adjacencies on random ordering polytopes and flow polytopes
论文作者
论文摘要
多重选择（MCP）是由于Block and Marschak（1960）引起的随机效用模型的预测范围。 Fishburn（1998）对当时的随机实用程序模型进行了很好的调查。 MCP的完整表征是Falmagne（1978）的非凡成就。除了Suck（2002）对方面的认可之外，MCP的几何结构显然没有太多研究。最近，Chang，Narita和Saito（2022）是指顶点的邻接，而Turansick（2022）使用的条件我们表明，这与两个顶点的非雅地相同。我们表征了顶点的邻接性和相邻的相邻。为了获得Falmagne定理的更具启发性的证据和吸吮结果，Fiorini（2004）用某些无环网络的流量层吸收了MCP。我们对邻接的结果也适用于任何无环网络的流层。特别是，它们不仅适用于MCP，还适用于戴维斯 - 斯托伯，Doignon，Fiorini，Glineur和Regenwetter（2018）的三个多层，作为弱级订单多层，间隔订单多层和semiorpoper的扩展公式提出，参见其他模型（其他模型的预测范围），例如Fishburn和Fishburn和Filmag和Falmag和20189年，以及20189年。
The Multiple Choice Polytope (MCP) is the prediction range of a random utility model due to Block and Marschak (1960). Fishburn (1998) offers a nice survey of the findings on random utility models at the time. A complete characterization of the MCP is a remarkable achievement of Falmagne (1978). Apart for a recognition of the facets by Suck (2002), the geometric structure of the MCP was apparently not much investigated. Recently, Chang, Narita and Saito (2022) refer to the adjacency of vertices while Turansick (2022) uses a condition which we show to be equivalent to the non-adjacency of two vertices. We characterize the adjacency of vertices and the adjacency of facets. To derive a more enlightening proof of Falmagne Theorem and of Suck result, Fiorini (2004) assimilates the MCP with the flow polytope of some acyclic network. Our results on adjacencies also hold for the flow polytope of any acyclic network. In particular, they apply not only to the MCP, but also to three polytopes which Davis-Stober, Doignon, Fiorini, Glineur and Regenwetter (2018) introduced as extended formulations of the weak order polytope, interval order polytope and semiorder polytope (the prediction ranges of other models, see for instance Fishburn and Falmagne, 1989, and Marley and Regenwetter, 2017).
