Name
Title | ||
|---|---|---|
Permutations in which pairs of numbers are not simultaneously close in position and close in size |
Abstract | ||
|---|---|---|
Let parallel to i, j parallel to(n) be the minimum of (i - j) mod n and (j - i) mod n. Given integers n and k, we seek a sequence a(0),..., a(n-1) which is a permutation of 0, 1,..., n-1 and such that whenever parallel to i, j parallel to(n) < s we have parallel to a(i), a(j)parallel to(n) >= k, with s as large as possible given k and n. We solve the problem completely when k divides n or k and n are relatively prime and in some other cases, but the problem remains open in general. We also consider the related problem in which parallel to i, j parallel to(n) < s is replaced with vertical bar i - j vertical bar < s and determine the maximum possible s for all cases of n and k. We also prove similar results for several extensions and variations of these problems. |
Year | Venue | DocType |
|---|---|---|
2020 | AUSTRALASIAN JOURNAL OF COMBINATORICS | Journal |
Volume | ISSN | Citations |
78 | 2202-3518 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Adam Mammoliti | 1 | 0 | 1.35 |
| Jamie Simpson | 2 | 0 | 0.34 |