96 citations · 190 across the 18 of their papers we have counts for
5 papers · 1 filter
On an identity of Sylvester
Bogdan Nica
We discuss an algebraic identity, due to Sylvester, as well as related algebraic identities and applications.
Polynomials over structured grids
Bogdan Nica
We study multivariate polynomials over `structured' grids. We begin by proposing an interpretation as to what it means for a finite subset of a field to be structured; we do so by…
A relative bound for independence
Bogdan Nica
We prove an upper bound for the independence number of a graph in terms of the largest Laplacian eigenvalue, and of a certain induced subgraph. Our bound is a refinement of a well-…
A brief introduction to Spectral Graph Theory
Bogdan Nica
Expanded lecture notes. Preliminary version, comments are welcome.
Unimodular graphs and Eisenstein sums
Bogdan Nica
Motivated in part by combinatorial applications to certain sum-product phenomena, we introduce unimodular graphs over finite fields and, more generally, over finite valuation rings…