8 citations · 14 across the 10 of their papers we have counts for
11 papers
Breaking the Infinite Barrier in the -- Conjecture
Max Aires, Swee Hong Chan, Igor Pak +1
The balance constant is a poset parameter measuring how well random linear extensions can be split according to their relative order on two elements. We give an -impro…
On the largest Littlewood--Richardson coefficient
Igor Pak, Daniel Soskin
We study partitions which attain the largest Littlewood-Richardson coefficient. More precisely, we prove that the largest is attained at partitions such that $μ\subseteq…
Quantum determinants in polynomial time
Igor Pak, Daniel Soskin
We give an algebraic branching program of polynomial size which computes Cayley determinant of right quantum matrices. This is a rare example of an efficient computation of a nonco…
Equality conditions for correlation inequalities
Swee Hong Chan, Igor Pak
We prove equality conditions for the Ahlswede--Daykin (AD) inequality and the Fortuin--Kasteleyn--Ginibre (FKG) inequality. We then present a number of applications and special cas…
Correlation inequalities for Schur positivity
Swee Hong Chan, Hong Chen, Igor Pak +1
We generalize the Ahlswede--Daykin inequality (1978) to a Schur positive \emph{ADS inequality}, which also contains the Lam--Postnikov--Pylyavskyy inequality (2007) as a special ca…
Effective resistance in planar graphs and continued fractions
Swee Hong Chan, Alex Kontorovich, Igor Pak
For a simple graph and edge , the effective resistance is defined as a ratio , where denotes the number of spanning trees in . We r…
Spanning trees and continued fractions
Swee Hong Chan, Alex Kontorovich, Igor Pak
We prove the exponential growth of the cardinality of the set of numbers of spanning trees in simple (and planar) graphs on vertices, answering a question of Sedláček from 1969…
Equality cases of the Stanley--Yan log-concave matroid inequality
Swee Hong Chan, Igor Pak
The \emph{Stanley--Yan} (SY) \emph{inequality} gives the ultra-log-concavity for the numbers of bases of a matroid which have given sizes of intersections with fixed disjoint s…
Linear extensions and continued fractions
Swee Hong Chan, Igor Pak
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the mi…
Linear extensions of finite posets
Swee Hong Chan, Igor Pak
We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subje…
Equality cases of the Alexandrov--Fenchel inequality are not in the polynomial hierarchy
Swee Hong Chan, Igor Pak
Describing the equality conditions of the Alexandrov--Fenchel inequality has been a major open problem for decades. We prove that in the case of convex polytopes, this description…