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COMBINATORICS
2002
15 years 3 months ago
2002
Let s(N) denote the edge length of the smallest square in which one can pack N unit squares. A duality method is introduced to prove that s(6) = s(7) = 3. Let nr be the smallest i...
146
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COMBINATORICS
1998
15 years 3 months ago
1998
A multimatroid is a combinatorial structure that encompasses matroids, delta-matroids and isotropic systems. This structure has been introduced to unify a theorem of Edmonds on th...
132
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COMBINATORICS
1998
15 years 3 months ago
1998
Using Zeilberger’s factorization of two-stack-sortable permutations, we write a functional equation — of a strange sort — that defines their generating function according t...
COMBINATORICS
1998
15 years 3 months ago
1998
The number of noncrossing partitions of {1, 2, . . . , n} with fixed block sizes has a simple closed form, given by Kreweras, and coincides with the corresponding number for nonne...
90
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COMBINATORICS
1998
15 years 3 months ago
1998
The Galois number Gn(q) is defined to be the number of subspaces of the n-dimensional vector space over the finite field GF(q). When q is prime, we prove that Gn(q) is equal to...