{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:33Z","timestamp":1759335813094,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Babson and Steingr\u00edmsson introduced generalized permutation patterns and showed that most of the Mahonian statistics in the literature can be expressed by\u00a0the combination of generalized pattern functions. Particularly, they defined\u00a0a new Mahonian statistic in terms of generalized pattern functions, which is denoted $stat$.\u00a0Given a permutation $\\pi$, let $des(\\pi)$ denote the\u00a0descent number of $\\pi$ and $maj(\\pi)$ denote\u00a0the major index of $\\pi$.\u00a0Babson and Steingr\u00edmsson conjectured that\u00a0$(des,stat)$ and $(des,maj)$ are equidistributed on $S_n$.\u00a0Foata and Zeilberger settled this conjecture using\u00a0q-enumeration, generating functions and Maple packages ROTA and PERCY.\u00a0Later, Burstein provided a bijective proof of a refinement of this conjecture.\u00a0In this paper, we give a new bijective proof of this conjecture.<\/jats:p>","DOI":"10.37236\/6411","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:58:08Z","timestamp":1578671888000},"source":"Crossref","is-referenced-by-count":2,"title":["A New Bijective Proof of Babson and Steingr\u00edmsson's Conjecture"],"prefix":"10.37236","volume":"24","author":[{"given":"Joanna N.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Shouxiao","family":"Li","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,4,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:02:21Z","timestamp":1579237341000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i2p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6411","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,4,13]]},"article-number":"P2.7"}}