R-critical numbers of natural intervals

Marcel Herzog, Gil Kaplan*, Arieh Lev, Romina Zigdon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The critical number cr(r, n) of natural intervals [r, n] was introduced by Herzog, Kaplan and Lev in 2014. The critical number cr(r, n) is the smallest integer t satisfying the following conditions: (i) every sequence of integers S = {r1 = r ≤ r2 ≤ · · · ≤ rk} with r1 +r2 +· · · +rk = n and k ≥ t has the following property: every integer between r and n − r can be written as a sum of distinct elements of S, and (ii) there exists S with k = t, which satisfies that property. In this paper we study a variation of the critical number cr(r, n) called the r-critical number rcr(r, n). We determine the value of rcr(r, n) for all r, n satisfying r | n.

Original languageEnglish
Article numberP4.42
JournalElectronic Journal of Combinatorics
Issue number4
StatePublished - 2021


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