TY - JOUR

T1 - R-critical numbers of natural intervals

AU - Herzog, Marcel

AU - Kaplan, Gil

AU - Lev, Arieh

AU - Zigdon, Romina

N1 - Publisher Copyright:
© The authors. Released under the CC BY-ND license (International 4.0).

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85120342075&partnerID=8YFLogxK

U2 - 10.37236/9835

DO - 10.37236/9835

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AN - SCOPUS:85120342075

SN - 1077-8926

VL - 28

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 4

M1 - P4.42

ER -