66 citations · 567 across the 83 of their papers we have counts for
89 papers
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…
Positive dependence for colored percolation
Nikita Gladkov, Igor Pak
For uniform random 4-colorings of graph edges with colors a,b,c,d, every two colors form a 1/2-percolation, and every two overlapping pairs of colors form independent 1/2-percolati…
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…
Algebraic and arithmetic properties of the cogrowth sequence of nilpotent groups
Igor Pak, David Soukup
We prove that congruences of the cogrowth sequence in a unitriangular group UT are undecidable. This is in contrast with abelian groups, where the congruences of the c…
What is a combinatorial interpretation?
Igor Pak
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Com…