{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:19:50Z","timestamp":1759335590795,"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>Let ${\\bf s} = (s_1, s_2, \\ldots, s_n,\\ldots)$ be a sequence of positive integers. An ${\\bf s}$-inversion sequence of length $n$ is a sequence ${\\bf e} = (e_1, e_2, \\ldots, e_n)$ of nonnegative integers such that $0 \\leq e_i &lt; s_i$ for $1\\leq i\\leq n$. When $s_i=(i-1)k+1$ for any $i\\geq 1$, we call the ${\\bf s}$-inversion sequences the $k$-inversion sequences. In this paper, we provide a bijective proof that the ascent number over $k$-inversion sequences of length $n$ is equidistributed with a weighted variant of the ascent number of permutations of order $n$, which leads to an affirmative answer of a question of Savage (2016). A key ingredient of the proof is a bijection between $k$-inversion sequences of length $n$ and $2\\times n$ arrays with particular restrictions. Moreover, we present a bijective proof of the fact that the ascent plateau number over $k$-Stirling permutations of order $n$ is equidistributed with the ascent number over $k$-inversion sequences of length $n$.<\/jats:p>","DOI":"10.37236\/8466","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:45:52Z","timestamp":1578638752000},"source":"Crossref","is-referenced-by-count":2,"title":["$1\/k$-Eulerian Polynomials and $k$-Inversion Sequences"],"prefix":"10.37236","volume":"26","author":[{"given":"Ting-Wei","family":"Chao","sequence":"first","affiliation":[]},{"given":"Jun","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Shi-Mei","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Yeong-Nan","family":"Yeh","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,8,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p35\/7895","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p35\/7895","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:09:36Z","timestamp":1579234176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i3p35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,16]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/8466","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,8,16]]},"article-number":"P3.35"}}