منابع مشابه
Generating Function for K-Restricted Jagged Partitions
We present a natural extension of Andrews’ multiple sums counting partitions of the form (λ1, · · · , λm) with λi ≥ λi+k−1 + 2. The multiple sum that we construct is the generating function for the so-called K-restricted jagged partitions. A jagged partition is a sequence of non-negative integers (n1, n2, · · · , nm) with nm ≥ 1 subject to the weakly decreasing conditions ni ≥ ni+1− 1 and ni ≥ ...
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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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We prove a known partitions theorem by Bell in an elementary and constructive way. Our proof yields a simple recursive method to compute the corresponding Sylvester polynomials for the partition. The previous known methods to obtain these polynomials are in general not elementary. 1. Proof of Bell's theorem. The main purpose of this section is to prove the following theorem, originally proved b...
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In [1] certain restricted partitions were studied in an elementary way. In this article we study other problem about restricted partitions. We prove the following theorem in a direct way and using elementary methods ( combinatory and mathematical induction). Theorem 1. Let n be a positive integer, and let A1, A2, . . . , An be n positive integers. Then, for all positive integers N = MK + r, the...
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Have you ever wondered how many ways the total of 5 dollars can be made with coins having cent values {1, 2, 5, 10, 20, 50, 100, 200}? Would you like to take a guess at how many ways there are? Would you be surprised if I told you there were 6295434? Maybe we should tone it down a bit and ask how many ways there are to make 50 cents. There are still 451! Lets step back once more and determine h...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2015
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-015-9704-x