{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:15:30Z","timestamp":1758824130002,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The notion of shuffle-compatible permutation statistics was implicit in Stanley's work on P-partitions and was first explicitly studied by Gessel and Zhuang. The aim of this paper is to prove that the triple ${\\rm (udr, pk, des)}$ is shuffle-compatible as conjectured by Gessel and Zhuang, where ${\\rm udr}$ denotes the number of up-down runs, ${\\rm pk}$ denotes the peak number, and ${\\rm des}$ denotes the descent number. This is accomplished by establishing an ${\\rm (udr, pk, des)}$-preserving bijection in the spirit of Baker-Jarvis and Sagan's bijective proofs of the shuffle compatibility property of permutation statistics.<\/jats:p>","DOI":"10.37236\/10953","type":"journal-article","created":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T08:36:39Z","timestamp":1656664599000},"source":"Crossref","is-referenced-by-count":2,"title":["On a Conjecture Concerning Shuffle-Compatible Permutation Statistics"],"prefix":"10.37236","volume":"29","author":[{"given":"Lihong","family":"Yang","sequence":"first","affiliation":[]},{"given":"Sherry H.F.","family":"Yan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,7,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T08:36:39Z","timestamp":1656664599000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i3p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,1]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/10953","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,7,1]]},"article-number":"P3.3"}}