Anti-Schur numbers for $\sum_{i=1}^{k-1} x_i = x_k$ in $[n]$
Fallon, Kean ; Giles, Colin ; Rehm, Hunter ; Wagner, Simon ; Warnberg, Nathan
arXiv, Tome 2019 (2019) no. 0, / Harvested from
Consider the set $\{1,2,\dots,n\} = [n]$ and an equation $eq$. The anti-Schur number, denoted $\operatorname{aS}([n],eq)$, is the smallest number of colors assigned to $[n]$ that guarantees a solution to $eq$ with every member of the solution set assigned a distinct color. This paper establishes the anti-Schur number for the equations $\sum_{i=1}^{k-1} x_i = x_k$ for $k=3$ and $k=4$. The paper also establishes a general lower bound for $k \ge 5$.
Publié le : 2019-01-24
Classification:  Mathematics - Combinatorics,  05 
@article{1901.08613,
     author = {Fallon, Kean and Giles, Colin and Rehm, Hunter and Wagner, Simon and Warnberg, Nathan},
     title = {Anti-Schur numbers for $\sum\_{i=1}^{k-1} x\_i = x\_k$ in $[n]$},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.08613}
}

Fallon, Kean; Giles, Colin; Rehm, Hunter; Wagner, Simon; Warnberg, Nathan. Anti-Schur numbers for $\sum_{i=1}^{k-1} x_i = x_k$ in $[n]$. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.08613/