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112
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COMBINATORICS
2006
15 years 5 months ago
2006
We show that matchings avoiding certain partial patterns are counted by the 3-Catalan numbers. We give a characterization of 12312-avoiding matchings in terms of restrictions on t...
132
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COMBINATORICS
2004
15 years 5 months ago
2004
The Sandwich Theorems proved in this paper give a new method to show that the partition function a(n) of a partition identity A(x) := n=0 a(n)xn = n=1 (1 - xn )-p(n) satisfies t...
158
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COMBINATORICS
2004
15 years 5 months ago
2004
The class of square (0, 1, -1)-matrices whose rows are nonzero and mutually orthogonal is studied. This class generalizes the classes of Hadamard and Weighing matrices. We prove t...
137
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COMBINATORICS
2004
15 years 5 months ago
2004
We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number o...
155
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COMBINATORICS
2004
15 years 5 months ago
2004
The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the p...