{
"id": "1901.00197",
"version": "v1",
"published": "2019-01-01T18:57:44.000Z",
"updated": "2019-01-01T18:57:44.000Z",
"title": "Is the Symmetric Group Sperner?",
"authors": [
"Larry H. Harper",
"Gene B. Kim"
],
"comment": "7 pages, 7 figures",
"categories": [
"math.CO"
],
"abstract": "An antichain A in a poset P is a subset of P in which no two elements are comparable. Sperner showed that the maximal antichain in the Boolean lattice, B_n, is the largest rank (of size n choose n/2). This type of problem has since been generalized, and a graded poset P is said to be Sperner if the largest rank of P is its maximal antichain. In this paper, we will show that the symmetric group S_n, partially ordered by refinement (or equivalently by absolute order), is Sperner.",
"revisions": [
{
"version": "v1",
"updated": "2019-01-01T18:57:44.000Z"
}
],
"analyses": {
"subjects": [
"05A05",
"05E99",
"60F05"
],
"keywords": [
"symmetric group sperner",
"maximal antichain",
"largest rank",
"boolean lattice",
"absolute order"
],
"note": {
"typesetting": "TeX",
"pages": 7,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}