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SUMMARY:Igor Pak (UCLA)
DTSTART:20211104T170000Z
DTEND:20211104T190000Z
DTSTAMP:20260422T015346Z
UID:CJCS/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/43/">Lo
 g-concave poset inequalities</a>\nby Igor Pak (UCLA) as part of Copenhagen
 -Jerusalem Combinatorics Seminar\n\n\nAbstract\nIn the ocean of log-concav
 e inequalities\, there are two islands that are especially difficult.  Fir
 st\, Mason's conjectures say that the number of forests in a graph with k 
 edges is log-concave.  More generally\, the number of independent sets of 
 size k in a matroid is log-concave.  Versions of these results were establ
 ished just recently\, in a remarkable series of papers inspired by algebra
 ic and geometric considerations.  Second\, Stanley's inequality for the nu
 mbers of linear extensions of a poset with value k at a given poset elemen
 t\, is log-concave.  This was originally conjectured by Chung\, Fishburn a
 nd Graham\, and proved by Stanley in 1981 using the Alexandrov–Fenchel i
 nequalities in convex geometry.  In our recent paper\, we present a new fr
 amework of combinatorial atlas which allows one to give elementary proofs 
 of both results\, and extend them in several directions.  I will give an i
 ntroduction to the area and then outline our approach.  Joint work with Sw
 ee Hong Chan.\n
LOCATION:https://researchseminars.org/talk/CJCS/43/
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