Chevyrev, Searles and Slinko: facets of comparative probability orders

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I. Chevyrev, D. Searles and A. Slinko, On the Number of Facets of Polytopes Representing Comparative Probability Orders, Order 30 (2013), no. 3, 749–761, DOI 10.1007/s11083-012-9274-0. The arXiv preprint, 1103.3938v1, dates from 21 March 2011. The journal version has not been compared.

Definitions 4–5, Theorem 3(a), and its construction were inspected in the arXiv version. They provide strict orders of subsets induced by positive weights, with at least $F_{k+1}$ flippable pairs on $k$ elements, where $F_1=F_2=1$. Each flippable pair is disjoint and adjacent in the same order. This is a source reading, not an independent proof audit.

The arXiv record, retrieved 2026-10-14, specifies arXiv's non-exclusive distribution license, with other rights reserved. No file of this source is held. No full transcription is provided under these terms.

Bears on. Problem 1100: the finite strict order persists when scaled weights are approximated by logarithms of distinct primes. Disjoint adjacent subsets then give coprime consecutive divisors of the squarefree product. The problem page records the complete author argument for this transfer and its source-dependent bound $g(k)\ge F_{k+1}$; it does not determine $g(k)$.