تقرير
The cross-product conjecture for width two posets
| العنوان: | The cross-product conjecture for width two posets |
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| المؤلفون: | Chan, Swee Hong, Pak, Igor, Panova, Greta |
| المصدر: | Trans. Amer. Math. Soc. 375 (2022), no. 8, 5923-5961 |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Probability, 05A20 (Primary) 05A30, 06A07, 06A11 (Secondary) |
| الوصف: | The cross--product conjecture (CPC) of Brightwell, Felsner and Trotter (1995) is a two-parameter quadratic inequality for the number of linear extensions of a poset $P= (X, \prec)$ with given value differences on three distinct elements in $X$. We give two different proofs of this inequality for posets of width two. The first proof is algebraic and generalizes CPC to a four-parameter family. The second proof is combinatorial and extends CPC to a $q$-analogue. Further applications include relationships between CPC and other poset inequalities, including a new $q$-analogue of the Kahn--Saks inequality. Comment: 31 pages, 7 figures. Counterexamples to Conjecture 11.2, 11.3, and 11.4 in v2 were found, and are now included in Section 11.5 and 11.10 of v3. To appear in Trans. Amer. Math. Soc |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1090/tran/8679 |
| URL الوصول: | http://arxiv.org/abs/2104.09009 |
| رقم الأكسشن: | edsarx.2104.09009 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1090/tran/8679 |
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