7 papers
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
The paper presents a polynomial‑size algebraic branching program that efficiently computes the Cayley determinant for right quantum matrices and its q‑generalizations, using combin…
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…
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 SedláÄek from 19…
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 . W…