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- W2017233617 abstract "In this paper we study the critical numbers c r ( r , n ) of natural intervals [ r , n ] . The critical number c r ( 1 , n ) is the smallest integer l satisfying the following conditions: (i) every sequence of integers S = { r 1 = 1 ⩽ r 2 ⩽ ⋯ ⩽ r k } with r 1 + ⋯ + r k = n and k ⩾ l has the following property: every integer between 1 and n can be written as a sum of distinct elements of S , and (ii) there exists S with k = l , satisfying this property. The definition of c r ( r , n ) for r > 1 is a natural extension of c r ( 1 , n ) . We completely determined the values of c r ( 1 , n ) and c r ( 2 , n ) . For r > 2 , we determined the values of c r ( r , n ) for n > 3 r 2 . Similar problems concerning subsets of finite groups were introduced by Erdös and Heilbronn in 1964 and extended by other authors." @default.
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- W2017233617 date "2014-05-01" @default.
- W2017233617 modified "2023-09-26" @default.
- W2017233617 title "Critical numbers of natural intervals" @default.
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- W2017233617 doi "https://doi.org/10.1016/j.jnt.2013.11.015" @default.
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