منابع مشابه
A note on triangle partitions
Koivisto studied the partitioning of sets of bounded cardinality. We improve his time analysis somewhat, for the special case of triangle partitions, and obtain a slight improvement.
متن کاملNote On 1-Crossing Partitions
of Kirkman (first proven by Cayley; see [7]) for the number of dissections of an n-gon using d diagonals. The goal here is to generalize Bóna’s result to count 1-crossing partitions by their number of blocks, and also to examine a natural q-analogue with regard to the cyclic sieving phenomenon shown in [8] for certain q-Catalan and q-Narayana numbers. The crux is the observation that 1-crossing...
متن کاملA Note on Modular Partitions and Necklaces
Following Jens Voß [9], let T (n, k) be the number of k-tuples u = (u1, u2, . . . , uk) with 0 ≤ u1 ≤ u2 ≤ · · · ≤ uk ≤ n− 1 such that ∑ j uj ≡ 0 mod n. Stated another way, T (n, k) is the number of ways to write 0 as a sum of k elements of Z/nZ. Voß calls u a modular partition of n into k parts. He computed the numbers T (n, k) for n+ k ≤ 20, and part of his table is shown here (the rows corre...
متن کاملGraphical Basis Partitions
A partition of an integer n is graphical if it is the degree sequence of a simple undirected graph It is an open question whether the fraction of partitions of n which are graphical approaches as n approaches in nity A partition is basic if the number of dots in its Ferrers graph is minimum among all partitions with the same rank vector as In this paper we investigate graphical partitions via b...
متن کاملOn the Number of Graphical Forest Partitions
A graphical partition of the even integer n is a partition of n where each part of the partition is the degree of a vertex in a simple graph and the degree sum of the graph is n. In this note, we consider the problem of enumerating a subset of these partitions, known as graphical forest partitions, graphical partitions whose parts are the degrees of the vertices of forests (disjoint unions of t...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1995
ISSN: 0095-8956
DOI: 10.1006/jctb.1995.1038