54 citations · 171 across the 31 of their papers we have counts for
6 papers · 1 filter
The Kauffman bracket of virtual links and the Bollobás-Riordan polynomial
Sergei Chmutov, Igor Pak
We show that the Kauffman bracket of a checkerboard colorable virtual link is an evaluation of the Bollobás-Riordan polynomial of a ribbon graph associated with…
An algebraic extension of the MacMahon Master Theorem
Pavel Etingof, Igor Pak
We present a new algebraic extension of the classical MacMahon Master Theorem. The basis of our extension is the Koszul duality for non-quadratic algebras defined by Berger. Combin…
Inflating the cube without stretching
Igor Pak
We give a simple proof of the following result: There exists a non-convex polyhedron whose surface is isometric to the surface of a cube of smaller volume.
Non-commutative extensions of the MacMahon Master Theorem
Matjaz Konvalinka, Igor Pak
We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-Le-Zeilberger. The proofs are combinat…
Groups of Intermediate Growth: an Introduction for Beginners
Rostislav Grigorchuk, Igor Pak
We present an accessible introduction to basic results on groups of intermediate growth.
A short proof of rigidity of convex polytopes
Igor Pak
We present a much simplified proof of Dehn's theorem on the infinitesimal rigidity of convex polytopes. Our approach is based on the ideas of Trushkina and Schramm.