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In the given example, there are 12 = 2(3!) permutations with property P 1, 6 = 3! permutations with property P 2 and no permutations have properties P 3 or P 4 as there are no restrictions for these two elements. The number of permutations satisfying the restrictions is thus: 4! − (12 + 6 + 0 + 0) + (4) = 24 − 18 + 4 = 10.
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The Birkhoff polytope B n (also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matching polytope of the complete bipartite graph , [1]) is the convex polytope in R N (where N = n 2) whose points are the doubly stochastic matrices, i.e., the n × n matrices whose entries are non-negative real numbers and whose rows and columns each add up to 1.
Microsoft Office 2007 (codenamed Office 12 [5]) is an office suite for Windows, developed and published by Microsoft. It was officially revealed on March 9, 2006 and was the 12th version of Microsoft Office .
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But as one Senate aide familiar with discussions on drone defense and policy told CNN, just because the drones aren’t directly impacting the military or military installations “doesn’t mean ...
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Bipartite networks are a particular class of complex networks, whose nodes are divided into two sets X and Y, and only connections between two nodes in different sets are allowed. For the convenience of directly showing the relation structure among a particular set of nodes, bipartite networks are usually compressed by one-mode projection.