{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T01:31:59Z","timestamp":1648517519867},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p>In this paper, we enumerate permutations [Formula: see text] according to the number of indices [Formula: see text] such that [Formula: see text], where [Formula: see text] and [Formula: see text] is a fixed positive integer. We term such an index [Formula: see text] an [Formula: see text]-impulse since it marks an occurrence where the bargraph representation of [Formula: see text] rises above (or to the same level as) the horizontal line [Formula: see text]. We find an explicit formula for the distribution as well as a formula for the total number of [Formula: see text]-impulses in all permutations of [Formula: see text]. Comparable distributions are also found for the [Formula: see text]-avoiding permutations of [Formula: see text], where [Formula: see text] is a pattern of length three. Two markedly different distributions emerge, one for [Formula: see text] and another for the remaining patterns in [Formula: see text]. In particular, we obtain a new equidistribution result between 123- and 132-avoiding permutations. To prove our results, we make use of multiple arrays and systems of functional equations, employing the kernel method to solve the system in the case [Formula: see text]. We also provide a combinatorial proof of the aforementioned equidistribution result, which actually applies to a more general class of multi-set permutations.<\/jats:p>","DOI":"10.1142\/s1793830918500544","type":"journal-article","created":{"date-parts":[[2018,6,14]],"date-time":"2018-06-14T03:51:04Z","timestamp":1528948264000},"page":"1850054","source":"Crossref","is-referenced-by-count":0,"title":["Impulse parameter and a new equivalence between 123- and 132-avoiding permutations"],"prefix":"10.1142","volume":"10","author":[{"given":"Toufik","family":"Mansour","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Haifa, 3498838 Haifa, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark","family":"Shattuck","sequence":"additional","affiliation":[{"name":"Institute for Computational Science &amp; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,7,30]]},"reference":[{"key":"S1793830918500544BIB001","doi-asserted-by":"crossref","first-page":"287","DOI":"10.26493\/1855-3974.600.5d2","volume":"9","author":"Blecher A.","year":"2015","journal-title":"Ars Math. 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