THE CROSS-PRODUCT CONJECTURE FOR WIDTH TWO POSETS

被引：2

作者：

Chan, Swee Hong ^{[1
]}

Pak, Igor ^{[1
]}

Panova, Greta ^{[2
]}

机构：

[1] UCLA, Dept Math, Los Angeles, CA 90095 USA

[2] USC, Dept Math, Los Angeles, CA 90089 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年

基金：

美国国家科学基金会;

关键词：

Linear extensions of posets; cross-product conjecture; 1/3-2/3; conjecture; Stanley inequality; Kahn-Saks inequality; Graham-Yao-Yao inequality; XYZ inequality; log-concavity; lattice path; Lindstrom-Gessel-Viennot lemma; q-analogue; MONOTONICITY PROPERTIES; INEQUALITY; SEQUENCES;

D O I：

10.1090/tran/8679

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The cross-product conjecture (CPC) of Brightwell, Felsner and Trotter [Order 12 (1995), pp. 327-349] is a two-parameter quadratic inequality for the number of linear extensions of a poset P = (X, (sic) )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, and the equality part of the CPC for posets of width two.

引用

页码：5923 / 5961

页数：39

共 50 条

[21] Using cross-product matrices to compute the SVD
Jia, Zhongxiao
[J]. NUMERICAL ALGORITHMS, 2006, 42 (01) : 31 - 61
[22] ANALYTICITY OF CROSS-PRODUCT BESSEL FUNCTION ZEROS
COCHRAN, JA
[J]. PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1966, 62 : 215 - &
[23] Advanced analysis techniques for cross-product coverage
Azatchi, H
Fournier, L
Ziv, A
Zohar, K
[J]. HLDVT'05: TENTH ANNUAL IEEE INTERNATIONAL HIGH-LEVEL DESIGN VALIDATION AND TEST WORKSHOP, PROCEEDINGS, 2005, : 229 - 236
[24] On posets of width two with positive Tits form
Bondarenko, Vitalij M.
Styopochkma, Marina V.
[J]. ALGEBRA & DISCRETE MATHEMATICS, 2005, (02): : 20 - 35
[25] CoVaC: Compiler validation by program analysis of the cross-product
Zaks, Anna
Pnueli, Amir
[J]. FM 2008: FORMAL METHODS, PROCEEDINGS, 2008, 5014 : 35 - +
[26] Remote scheme for password authentication based on cross-product
Tan, Kaijun
He, Chen
Zhu, Hongwen
[J]. Tien Tzu Hsueh Pao/Acta Electronica Sinica, 2000, 28 (02): : 28 - 30
[27] Vector Sensor Cross-product for Direction of Arrival Estimation
Sun, Li
Ou, Gang
Lu, Yilong
[J]. PROCEEDINGS OF THE 2009 2ND INTERNATIONAL CONGRESS ON IMAGE AND SIGNAL PROCESSING, VOLS 1-9, 2009, : 4713 - +
[28] Radii of starlikeness and convexity of a cross-product of Bessel functions
Baricz, Arpad
Yagmur, Nihat
[J]. RAMANUJAN JOURNAL, 2017, 44 (03): : 493 - 519
[29] THE LINEAR DISCREPANCY OF A PRODUCT OF TWO POSETS
Cheong, Minseok
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (03) : 1081 - 1094
[30] Cross-product manipulation with intertemporal constraints: An equilibrium model
Guo, Nongchao
Lo Prete, Chiara
[J]. ENERGY POLICY, 2019, 134

← 1 2 3 4 5 →