{
"id": "1708.09109",
"version": "v1",
"published": "2017-08-30T04:33:42.000Z",
"updated": "2017-08-30T04:33:42.000Z",
"title": "Hook length property of $d$-complete posets via $q$-integrals",
"authors": [
"Jang Soo Kim",
"Meesue Yoo"
],
"comment": "40 pages, 28 figures",
"categories": [
"math.CO",
"math.CA"
],
"abstract": "The hook length formula for $d$-complete posets states that the $P$-partition generating function for them is given by a product in terms of hook lengths. We give a new proof of the hook length formula using $q$-integrals. The proof is done by a case-by-case analysis consisting of two steps. First, we express the $P$-partition generating function for each case as a $q$-integral and then we evaluate the $q$-integrals. Several $q$-integrals are evaluated using partial fraction expansion identities and others are verified by computer.",
"revisions": [
{
"version": "v1",
"updated": "2017-08-30T04:33:42.000Z"
}
],
"analyses": {
"subjects": [
"06A07",
"05A30",
"05A15"
],
"keywords": [
"hook length property",
"hook length formula",
"partition generating function",
"partial fraction expansion identities",
"complete posets states"
],
"note": {
"typesetting": "TeX",
"pages": 40,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}