Partitions and diamond
نویسندگان
چکیده
منابع مشابه
PARITY RESULTS FOR BROKEN k–DIAMOND PARTITIONS AND (2k + 1)–CORES
In this paper we prove several new parity results for broken k-diamond partitions introduced in 2007 by Andrews and Paule. In the process, we also prove numerous congruence properties for (2k+1)-core partitions. The proof technique involves a general lemma on congruences which is based on modular forms.
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Article history: Received 28 April 2014 Received in revised form 14 October 2014 Accepted 14 October 2014 Available online 31 October 2014 MSC: 54D20
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We consider two kinds of partition of a graph, namely orbit partitions and equitable partitions. Although an orbit partition is always an equitable partition, the converse is not true in general. We look at some classes of graphs for which the converse is true.
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A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
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Rhombellanes are mathematical structures existing in various environments, in crystal or quasicrystal networks, or even in their homeomorphs, further possible becoming real molecules. Rhombellanes originate in the K2.3 complete bipartite graph, a tile found in the linear polymeric staffanes. In close analogy, a rod-like polymer derived from hexahydroxy-cyclohexane was imagined. Further, the ide...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1986
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1986-0831401-8