BEGIN:VCALENDAR
CALSCALE:GREGORIAN
PRODID:iCalendar-Ruby
VERSION:2.0
BEGIN:VEVENT
DESCRIPTION: A famous and wide-open problem\, going back to at least the ea
 rly 1970's\, concerns the classification of chromatic polynomials of graphs
 . Toward this classification problem\, one may ask for necessary inequaliti
 es among the coefficients of a chromatic polynomial\, and we contribute one
  such set of inequalities when a chromatic polynomial $\chi_G(n) = \chi^*_0
  \binom {n+d} d + \chi^*_1 \binom {n+d-1} d + \dots + \chi^*_d \binom n d$ 
 is written in terms of a binomial-coefficient basis. More precisely\, we pr
 ove that $\chi^*_{d-2}+\chi^*_{d-3}+\dots+\chi^*_{d-j-1} \ \ge \ \chi^*_1+\
 chi^*_2+\dots+\chi^*_j $\, for $1 \le j \le \lfloor \frac{ d }{ 2 } \rfloor
  - 1$. A similar result holds for flow polynomials enumerating either modul
 ar or integral nowhere-zero flows of a graph. Our theorems follow from conn
 ections among chromatic\, flow\, order\, and Ehrhart polynomials\, and the 
 fact that the latter satisfy a decomposition formula into symmetric polynom
 ials due to Stapledon.   (This is joint work with Emerson Le\'on.) 
DTSTAMP:20181105T173500
DTSTART:20180625T160000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin Institut für Mathematik Straße des 1
 7. Juni 136 10623 Berlin room MA 041 (ground floor)
SEQUENCE:0
SUMMARY:Matthias Beck: Binomial Inequalities of Chromatic\, Flow\, and Ehrh
 art Polynomials
UID:89808499@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20180625-L-Bec
 k.html
END:VEVENT
END:VCALENDAR