查看“︁凡得瓦登猜想”︁的源代码

在[[线性代数]]中，'''Van der Waerden猜想'''是一个关于[[积和式]]的命题，其具体内容如下：

{{Squote|w=80%|对于任意的双[[轉移矩陣]]，其[[积和式]]的值大于等于<math>n!/n^n</math>。}}

注意到该下界在所有元素均为<math>1/n</math>时成立。该猜想由{{link-en|Bartel Leendert van der Waerden}}在1926年提出<ref>{{citation
 | last = van der Waerden | first = B. L. | author-link = Bartel Leendert van der Waerden
 | journal = Jber. Deutsch. Math.-Verein.
 | page = 117
 | title = Aufgabe 45
 | volume = 35
 | year = 1926}}.</ref>，在1980年由B. Gyires<ref>{{citation
 | last = Gyires | first = B.
 | issue = 3-4
 | journal = Publicationes Mathematicae Institutum Mathematicum Universitatis Debreceniensis
 | mr = 604006
 | pages = 291–304
 | title = The common source of several inequalities concerning doubly stochastic matrices
 | volume = 27
 | year = 1980}}.</ref>，1981年由G. P. Egorychev<ref>{{citation
 | last = Egoryčev | first = G. P.
 | language = ru
 | location = Krasnoyarsk
 | mr = 602332
 | page = 12
 | publisher = Akad. Nauk SSSR Sibirsk. Otdel. Inst. Fiz.
 | title = Reshenie problemy van-der-Vardena dlya permanentov
 | year = 1980}}. {{citation
 | last = Egorychev | first = G. P.
 | issue = 6
 | journal = Akademiya Nauk SSSR
 | language = ru
 | mr = 638007
 | pages = 65–71, 225
 | title = Proof of the van der Waerden conjecture for permanents
 | volume = 22
 | year = 1981}}. {{citation
 | last = Egorychev | first = G. P.
 | doi = 10.1016/0001-8708(81)90044-X
 | issue = 3
 | journal = Advances in Mathematics
 | mr = 642395
 | pages = 299–305
 | title = The solution of van der Waerden's problem for permanents
 | volume = 42
 | year = 1981}}.</ref>和D. I. Falikman<ref>{{citation
 | last = Falikman | first = D. I.
 | issue = 6
 | journal = Akademiya Nauk Soyuza SSR
 | language = ru
 | mr = 625097
 | pages = 931–938, 957
 | title = Proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix
 | volume = 29
 | year = 1981}}.</ref>独立证明，其中Egorychev的证明用到了{{link-en|Alexandrov–Fenchel不等式|Alexandrov–Fenchel inequality}}。<ref name=CMC487>Brualdi (2006) p.487</ref>由于这项工作，Egorychev和Falikman赢得了1982年的{{link-en|Fulkerson奖|Fulkerson Prize}}。<ref>[http://www.mathopt.org/?nav=fulkerson Fulkerson Prize] {{Wayback|url=http://www.mathopt.org/?nav=fulkerson |date=20190212173654 }}, Mathematical Optimization Society, retrieved 2012-08-19.</ref>

== 参考 ==
<references/>

[[Category:猜想]]
[[Category:多項式]]
[[Category:線性代數]]