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COMBINATORICS
2002
15 years 3 months ago
2002
Let In() denote the number of involutions in the symmetric group Sn which avoid the permutation . We say that two permutations , Sj may be exchanged if for every n, k, and order...
132
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COMBINATORICS
2002
15 years 3 months ago
2002
The directed anti-Oberwolfach problem asks for a 2-factorization (each factor has in-degree 1 and out-degree 1 for a total degree of two) of K2n+1, not with consistent cycle compo...
132
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COMBINATORICS
1998
15 years 3 months ago
1998
Let α and β be a partition of {1, . . . , n} into two blocks. A merging network is a network of comparators which allows as input arbitrary real numbers and has the property tha...
101
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COMBINATORICS
1998
15 years 3 months ago
1998
Let F(n) be a family of partitions of n and let F(n d) denote the set of partitions in F(n) with Durfee square of size d. We de ne the Durfee polynomial of F(n) to be the polynomi...
107
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COMBINATORICS
1998
15 years 3 months ago
1998
: Following Frankl and F¨uredi [1] we say a family, F, of subsets of an n-set is weakly union-free if F does not contain four distinct sets A, B, C, D with A ∪ B = C ∪ D. If i...