BEGIN:VCALENDAR
VERSION:2.0
METHOD:PUBLISH
PRODID:-//Virginia Tech//VT Calendar//EN
BEGIN:VEVENT
DTSTAMP:20201007T200000Z
UID:1601903941411@events.msu.edu
CATEGORIES:Conferences / Seminars / Lectures
DTSTART:20201007T200000Z
DTEND:20201007T210000Z
SUMMARY:Math Seminar Series
DESCRIPTION:
 Seminar in Cluster algebras\n
 \n
 Bruce E. Sagan 
 will be speaking.\n
 \n
 The presentation is titled 
 "On a rank-unimodality conjecture of Morier-Genoud 
 and Ovsienko."\n
 \n
 This is a virtual 
 meeting that will be held over Zoom.\n
 \n
 The description 
 is as follows:\n
 Let α=(a,b,...) 
 be a composition. Consider the associated 
 poset F(α), called a fence, whose covering 
 relations are x1⊲x2⊲...⊲xa+1⊳xa+2⊳...⊳xa+b+1⊲xa+b+2⊲... 
 .\n
 We study the associated distributive 
 lattice L(α) consisting of all 
 lower order ideals of F(α). These lattices 
 are important in the theory of cluster 
 algebras and their rank generating functions 
 can be used to define q-analogues of rational 
 numbers. In particular, we make progress on 
 a recent conjecture of Morier-Genoud and Ovsienko 
 that L(α) is rank unimodal. We show 
 that if one of the parts of α is greater 
 than the sum of the others, then the conjecture 
 is true. We conjecture that L(α) enjoys 
 the stronger properties of having a nested 
 chain decomposition and having a rank sequence 
 which is either top or bottom interlacing, 
 the latter being a recently defined property 
 of sequences. We verify that these properties 
 hold for compositions with at most three 
 parts and for what we call d-divided posets, 
 generalizing work of Claussen and simplifying 
 a construction of Gansner.\n\n
 Price: free\n
 Sponsor: Department of Mathematics\n
 Sponsor's Homepage: https://www.math.msu.edu/\n
 Contact name: Department of Mathematics\n
 Contact phone: (517) 353-0844\n
 for more info visit the web at:\n 
 https://www.math.msu.edu/Seminars/CalendarView.aspx?month-of=September2016\n
LOCATION:Zoom link provided on Math Seminars page
END:VEVENT
END:VCALENDAR