3 citations · 5 across the 6 of their papers we have counts for
6 papers
A combinatorial proof of the Rogers-Ramanujan and Schur identities
Cilanne Boulet, Igor Pak
We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direct bij…
Reductions of Young tableau bijections
Igor Pak, Ernesto Vallejo
We introduce notions of linear reduction and linear equivalence of bijections for the purposes of study bijections between Young tableaux. Originating in Theoretical Computer Scien…
The area of cyclic polygons: Recent progress on Robbins' Conjectures
Igor Pak
In his works [R1,R2] David Robbins proposed several interrelated conjectures on the area of the polygons inscribed in a circle as an algebraic function of its sides. Most recently,…
Combinatorics and geometry of Littlewood-Richardson cones
Igor Pak, Ernesto Vallejo
We present several direct bijections between different combinatorial interpretations of the Littlewood-Richardson coefficients. The bijections are defined by explicit linear maps w…
Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings
Ezra Miller, Igor Pak
This paper is a study of the interaction between the combinatorics of boundaries of convex polytopes in arbitrary dimension and their metric geometry. Let S be the boundary of a co…
Bijections for refined restricted permutations
Sergi Elizalde, Igor Pak
We present a bijection between 321- and 132-avoiding permutations that preserves the number of fixed points and the number of excedances. This gives a simple combinatorial proof of…