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SUMMARY:Isabelle Shankar (UC Berkeley)
DTSTART:20200413T191000Z
DTEND:20200413T200000Z
DTSTAMP:20260404T095206Z
UID:BerkeleyCombinatorics/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Berke
 leyCombinatorics/1/">An SOS counterexample to an inequality of symmetric f
 unctions</a>\nby Isabelle Shankar (UC Berkeley) as part of The UC Berkeley
  combinatorics seminar\n\nLecture held in 939 Evans Hall.\n\nAbstract\nIt 
 is known that differences of symmetric functions corresponding to various 
 bases are nonnegative on the nonnegative orthant exactly when the partitio
 ns defining them are comparable in dominance order. The only exception is 
 the case of homogeneous symmetric functions where it is only known that do
 minance of the partitions implies nonnegativity of the corresponding diffe
 rence of symmetric functions. It was conjectured by Cuttler\, Greene\, and
  Skandera in 2011 that the converse also holds\, as in the cases of the mo
 nomial\, elementary\, power-sum\, and Schur bases. I will derive a counter
 example using the theory of sum of squares relaxations and thus show that 
 homogeneous symmetric functions break the pattern.\n
LOCATION:https://stable.researchseminars.org/talk/BerkeleyCombinatorics/1/
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SUMMARY:Robert Scherer (UC Davis)
DTSTART:20200420T191000Z
DTEND:20200420T200000Z
DTSTAMP:20260404T095206Z
UID:BerkeleyCombinatorics/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Berke
 leyCombinatorics/2/">A criterion for asymptotic sharpness in the enumerati
 on of simply generated trees</a>\nby Robert Scherer (UC Davis) as part of 
 The UC Berkeley combinatorics seminar\n\nLecture held in 939 Evans Hall.\n
 \nAbstract\nWe study the identity y(x) = xA(y(x))\, from the theory of roo
 ted trees\, for appropriate generating functions y(x) and A(x) with non-ne
 gative integer coefficients. A problem that has been studied extensively i
 s to determine the asymptotics of the coefficients of y(x) from analytic p
 roperties of the complex function z 􏰀→ A(z)\, assumed to have a posit
 ive radius of convergence R. It is well-known that the vanishing of A(x) 
 − xA′(x) on (0\, R) is sufficient to ensure that y(r) < R\, where r is
  the radius of convergence of y(x). This result has been generalized in th
 e literature to account for more general functional equations than the one
  above\, and used to determine asymptotics for the Taylor coefficients of 
 y(x). What has not been shown is whether that sufficient condition is also
  necessary. We show here that it is\, thus establishing a criterion for sh
 arpness of the inequality y(r) ≤ R. As an application\, we prove a 1996 
 conjecture of Kuperberg regarding the asymptotic growth rate of an integer
  sequence arising in the study of Lie algebra representations.\n
LOCATION:https://stable.researchseminars.org/talk/BerkeleyCombinatorics/2/
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BEGIN:VEVENT
SUMMARY:Jesus de Loera (UC Davis)
DTSTART:20200427T191000Z
DTEND:20200427T200000Z
DTSTAMP:20260404T095206Z
UID:BerkeleyCombinatorics/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Berke
 leyCombinatorics/3/">Combinatorics on the space of monotone paths of a pol
 ytope</a>\nby Jesus de Loera (UC Davis) as part of The UC Berkeley combina
 torics seminar\n\nLecture held in 939 Evans Hall.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BerkeleyCombinatorics/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Pawlowski (USC)
DTSTART:20200406T191000Z
DTEND:20200406T200000Z
DTSTAMP:20260404T095206Z
UID:BerkeleyCombinatorics/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Berke
 leyCombinatorics/5/">The fraction of an Sn-orbit on a hyperplane</a>\nby B
 rendan Pawlowski (USC) as part of The UC Berkeley combinatorics seminar\n\
 nLecture held in 939 Evans Hall.\n\nAbstract\nHuang\, McKinnon\, and Satri
 ano conjectured that if a real vector $(v_1\,...\,v_n)$ has distinct coord
 inates and $n\\ge3$\, then a hyperplane through the origin other than $x_1
 +...+x_n=0$ contains at most $2(n−2)!\\lfloor n/2\\rfloor$ of the vector
 s obtained by permuting the coordinates of $v$. I will discuss a proof of 
 this conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/BerkeleyCombinatorics/5/
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