BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Brian Hopkins (Saint Peter's University) DTSTART:20200605T173000Z DTEND:20200605T175500Z DTSTAMP:20260423T011157Z UID:CANT2020/64 DESCRIPTION:Title: Restricted multicompositions\nby Brian Hopkins (Saint Peter's Univer sity) as part of Combinatorial and additive number theory (CANT 2021)\n\n\ nAbstract\nIn 2007\, George Andrews introduced $k$-compositions\, \na gene ralization of integer compositions\, where each summand has $k$ possible c olors\, \nexcept for the final part which must be color 1. Last year\, St \\'ephane Ouvry and \nAlexios Polychronakos introduced $g$-compositions wh ich allow for up to $g-2$ zeros \nbetween parts. Although these do not ha ve the same definition and came from very different\nmotivations (number t heory and quantum mechanics\, respectively)\, \nwe will see that they are equivalent. One reason these are compelling combinatorial objects \nis th eir count: there are $(k+1)^{n-1}$ $k$-compositions of $n$. \nResults fro m standard integer compositions can have interesting generalizations. \nF or example\, there are three types of restricted compositions counted by F ibonacci \nnumbers---parts 1 & 2\, odd parts\, and parts greater than 1. We will explore the diverging \nfamilies of recurrences that arise from ap plying these restrictions to multicompositions.\n LOCATION:https://researchseminars.org/talk/CANT2020/64/ END:VEVENT END:VCALENDAR