Balanced matrix: Difference between revisions

Revision as of 00:27, 6 August 2010

Revision as of 01:57, 7 August 2010

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==Subsequence count==

An alternative method of identifying a balanced matrix that is also a zero-one matrix is through the subsequence count, where the subsequence count ''SC'' of any row s of matrix ''A'' is

:'''SC''' = |{''t'' | [''a''_''sj''&nbsp;=&nbsp;1, ''a''_''ij''&nbsp;=&nbsp;0 for ''s''&nbsp;<&nbsp;''i''&nbsp;<&nbsp;''t'', ''a''_''tj''&nbsp;=&nbsp;1], ''j''&nbsp;=&nbsp;1,&nbsp;...,&nbsp;''n''}|

If a matrix ''A'' has SC(s) <= 1 for all rows s = 1,...,m, then A has a unique subsequence, and is also balanced.

If a matrix ''A'' has SC(''s'') <= &nbsp;≤&nbsp;1 for all rows ''s ''&nbsp;= &nbsp;1,&nbsp;...,&nbsp;''m'', then ''A'' has a unique subsequence, and is also balanced.

== References ==