{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:54Z","timestamp":1753893834469,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the classical Mahonian statistics on the set $B_n(\\Sigma)$ of signed permutations in the hyperoctahedral group $B_n$ which avoid all patterns in $\\Sigma$, where $\\Sigma$ is a set of patterns of length two. \u00a0In 2000, Simion gave the cardinality of $B_n(\\Sigma)$ in the cases where $\\Sigma$ contains either one or two patterns of length two and showed that $\\left|B_n(\\Sigma)\\right|$ is constant whenever $\\left|\\Sigma\\right|=1$, whereas in most but not all instances where $\\left|\\Sigma\\right|=2$, $\\left|B_n(\\Sigma)\\right|=(n+1)!$. \u00a0We answer an open question of Simion by providing bijections from $B_n(\\Sigma)$ to $S_{n+1}$ in these cases where $\\left|B_n(\\Sigma)\\right|=(n+1)!$. \u00a0In addition, we extend Simion's work by providing a combinatorial proof in the language of signed permutations for the major index on $B_n(21, \\bar{2}\\bar{1})$ and by giving the major index on $D_n(\\Sigma)$ for $\\Sigma =\\{21, \\bar{2}\\bar{1}\\}$ and $\\Sigma=\\{12,21\\}$. \u00a0The main result of this paper is to give the inversion generating functions for $B_n(\\Sigma)$ for almost all sets $\\Sigma$ with $\\left|\\Sigma\\right|\\leq2.$<\/jats:p>","DOI":"10.37236\/6545","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:15:46Z","timestamp":1578683746000},"source":"Crossref","is-referenced-by-count":0,"title":["Inversion Generating Functions for Signed Pattern Avoiding Permutations"],"prefix":"10.37236","volume":"24","author":[{"given":"Naiomi T.","family":"Cameron","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kendra","family":"Killpatrick","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2017,2,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p39\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:04:05Z","timestamp":1579237445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,17]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/6545","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,2,17]]},"article-number":"P1.39"}}