更改

==Block designs==

==Block designs==

'''<font color="#ff8000">区组设计/块设计 Block Designs</font>'''

'''<font color="#ff8000">区组设计/块设计 Block Designs</font>'''<br>

 

Another example is a [[block design]]. Here ''X'' is a finite set of "points" and ''Y'' is a class of subsets of ''X'', called "blocks", subject to rules that depend on the type of design. The incidence matrix is an important tool in the theory of block designs. For instance, it can be used to prove [[Fisher's inequality]], a fundamental theorem of balanced incomplete 2-designs (BIBDs), that the number of blocks is at least the number of points.<ref>{{citation|page=99|first=Herbert John|last=Ryser|title=Combinatorial Mathematics|series=The Carus Mathematical Monographs #14|publisher=The Mathematical Association of America|year=1963}}</ref> Considering the blocks as a system of sets, the [[Permanent (mathematics)|permanent]] of the incidence matrix is the number of [[system of distinct representatives|systems of distinct representatives]] (SDRs).

Another example is a [[block design]]. Here ''X'' is a finite set of "points" and ''Y'' is a class of subsets of ''X'', called "blocks", subject to rules that depend on the type of design. The incidence matrix is an important tool in the theory of block designs. For instance, it can be used to prove [[Fisher's inequality]], a fundamental theorem of balanced incomplete 2-designs (BIBDs), that the number of blocks is at least the number of points.<ref>{{citation|page=99|first=Herbert John|last=Ryser|title=Combinatorial Mathematics|series=The Carus Mathematical Monographs #14|publisher=The Mathematical Association of America|year=1963}}</ref> Considering the blocks as a system of sets, the [[Permanent (mathematics)|permanent]] of the incidence matrix is the number of [[system of distinct representatives|systems of distinct representatives]] (SDRs).