منابع مشابه
Strongly intersecting integer partitions
We call a sum a1 + a2 + · · ·+ ak a partition of n of length k if a1, a2, . . . , ak and n are positive integers such that a1 ≤ a2 ≤ · · · ≤ ak and n = a1 + a2 + · · ·+ ak. For i = 1, 2, . . . , k, we call ai the i-th part of the sum a1 + a2 + · · ·+ ak. Let Pn,k be the set of all partitions of n of length k. We say that two partitions a1 + a2 + · · · + ak and b1 + b2 + · · ·+ bk strongly inter...
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If a1, a2, . . . , ak and n are positive integers such that n = a1+a2+· · ·+ak, then the sum a1 + a2 + · · ·+ ak is said to be a partition of n of length k, and a1, a2, . . . , ak are said to be the parts of the partition. Two partitions that differ only in the order of their parts are considered to be the same partition. Let Pn be the set of partitions of n, and let Pn,k be the set of partitio...
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Let denote the positive octant of the regular -dimensional cubic lattice. Each vertex (1 2 ) of is adjacent to all vertices of the form (1 2 + 1 ), 1 ≤ ≤ . A -partition of a positive integer is an assignment of nonnegative integers 12 to the vertices of , subject to both an ordering condition 12 ≥ max 1≤≤ 12+...
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Let m, n and t be positive integers. Consider [m] as the set of sequences of length n on an m-letter alphabet. We say that two subsets A ⊂ [m] and B ⊂ [m] cross t-intersect if any two sequences a ∈ A and b ∈ B match in at least t positions. In this case we show that if m > (1 − 1 t 2 ) −1 then |A||B| ≤ (mn−t)2. One of our main tools is the eigenvalue method for intersection matrices due to Frie...
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2000, under the auspices of the Pacific Institute for the Mathematical Sciences. My original intent was to describe the sequence of developments which began in the 1980's and has led to a unified and automated approach to finding partition bijections. These developments, of six papers, in fact form much of the content of these notes, but it seemed desirable to preface them with some general bac...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.07.018