Posts tagged: combinatorics

I recently got introduced to this game called Can't Stop and it got me thinking about probabilities. You know how it is - you start playing a dice game and suddenly you're knee-deep in combinatorics...

Let's say we have a graph (i.e. network), and we want to cluster the vertices (nodes).  Here, think of the nodes as people, agents, oscillators, some dynamic being, and the edges... the edges tell...

It always excites me when I see a combinatorial matrix theory problem, and this is no exception, though it is so basic that it shows up in all forms and shapes. Let me start with a combinatorial...

My friend asked me this: Put balls into $n$ buckets uniformly at random and count $h$ the number of buckets with at least one ball in them. What is the expected value of number of balls $k$?

In a huge graph, it is hard to determine a bottleneck by just looking at it, or doing any type of search. And by a bottleneck, I mean part of graph that is not very much connected to the other part....

My first solo paper "Existence of a Not Necessarily Symmetric Matrix with Given Distinct Eigenvalues and Graph" got published in Journal of Linear Algebra and its Applications, yesterday. It took it...

We started the project in Graduate Research Workshop in Combinatorics (Rocky Mountain Great Plains GRWC) in summer 2014, hosted by University of Denver and University of Colorado Denver. Two weeks of...

If you have a prime number $p$ (other than two and five) then the last digit of $p$ is 1, 3, 7, or 9. If for some reason we believe that prime numbers are randomly distributed (after all, the last...

I went to several talks and meetings in the past few days, and I am going to talk about some of them, but first let me start with some predicting game:

Dmitry Ryabogin from Kent State University gave two talks today here at UCalgray. The first talk was about convex bodies with congruent projections. You can read about it here: PDF. And their recent...

For the past several months my Saturdays consist of two meetings, each of which about 4 hours long, with two of my colleagues working on various problems. Clearly we've hit a lot of dead ends, and...

We (Sudipta Mallik and I) just submitted our paper on the "Spectral characterization of matchings in graphs". It is based on our previous work on "Construction of real skew-symmetric matrices from...