13 citations · 113 across the 34 of their papers we have counts for
36 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…
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…
Independent Sets and Continued Fractions
Swee Hong Chan, Steven Heilman, Greta Panova
Linek's 1989 problem asks whether the numbers of independent sets of trees avoid infinitely many positive integers. We show that the set of natural numbers realized as the number o…
Normalized matching property for competing urn models
Swee Hong Chan
We study the competing urn model in which balls are placed independently into urns according to (possibly distinct) ball distributions. Kahn and Neiman (2010) showed that,…
Unimodality for Radon partitions of random vectors
Swee Hong Chan, Gil Kalai, Bhargav Narayanan +2
Consider the (almost surely) unique Radon partition of a set of random Gaussian vectors in ; choose one of the two parts of this partition uniformly at random,…
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…
Computational complexity of counting coincidences
Swee Hong Chan, Igor Pak
Can you decide if there is a coincidence in the numbers counting two different combinatorial objects? For example, can you decide if two regions in have the same num…
On the cross-product conjecture for the number of linear extensions
Swee Hong Chan, Igor Pak, Greta Panova
We prove a weak version of the cross--product conjecture: , where is the number of…
Multivariate correlation inequalities for -partitions
Swee Hong Chan, Igor Pak
Motivated by the Lam--Pylyavskyy inequalities for Schur functions, we give a far reaching multivariate generalization of Fishburn's correlation inequality for the number of linear…
Correlation inequalities for linear extensions
Swee Hong Chan, Igor Pak
We employ the combinatorial atlas technology to prove new correlation inequalities for the number of linear extensions of finite posets. These include the approximate independence…
Effective poset inequalities
Swee Hong Chan, Igor Pak, Greta Panova
We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Björner--Wachs inequality and generalize it to inequalities on…
Introduction to the combinatorial atlas
Swee Hong Chan, Igor Pak
We give elementary self-contained proofs of the strong Mason conjecture recently proved by Anari at. al. (arXiv:1811.01600) and Brändén--Huh (arXiv:1902.03719), and of the classica…
Log-concave poset inequalities
Swee Hong Chan, Igor Pak
We study combinatorial inequalities for various classes of set systems: matroids, polymatroids, poset antimatroids, and interval greedoids. We prove log-concavity inequalities for…
Log-concavity in planar random walks
Swee Hong Chan, Igor Pak, Greta Panova
We prove log-concavity of exit probabilities of lattice random walks in certain planar regions.
Extensions of the Kahn--Saks inequality for posets of width two
Swee Hong Chan, Igor Pak, Greta Panova
The Kahn--Saks inequality is a classical result on the number of linear extensions of finite posets. We give a new proof of this inequality for posets of width two using explicit i…
The cross-product conjecture for width two posets
Swee Hong Chan, Igor Pak, Greta Panova
The cross--product conjecture (CPC) of Brightwell, Felsner and Trotter (1995) is a two-parameter quadratic inequality for the number of linear extensions of a poset …
Recurrence of horizontal-vertical walks
Swee Hong Chan
Consider a nearest neighbor random walk on the two-dimensional integer lattice, where each vertex is initially labeled either `H' or `V', uniformly and independently. At each discr…
Sorting probability of Catalan posets
Swee Hong Chan, Igor Pak, Greta Panova
We show that the sorting probability of the Catalan poset} satisfies .