193 research outputs found
A result on polynomials derived via graph theory
We present an example of a result in graph theory that is used to obtain a
result in another branch of mathematics. More precisely, we show that the
isomorphism of certain directed graphs implies that some trinomials over finite
fields have the same number of roots
A hierarchy of randomness for graphs
AbstractIn this paper we formulate four families of problems with which we aim at distinguishing different levels of randomness.The first one is completely non-random, being the ordinary Ramsey–Turán problem and in the subsequent three problems we formulate some randomized variations of it. As we will show, these four levels form a hierarchy. In a continuation of this paper we shall prove some further theorems and discuss some further, related problems
Closed expressions for averages of set partition statistics
In studying the enumerative theory of super characters' of the group of upper
triangular matrices over a finite field we found that the moments (mean,
variance and higher moments) of novel statistics on set partitions have simple
closed expressions as linear combinations of shifted bell numbers. It is shown
here that families of other statistics have similar moments. The coefficients
in the linear combinations are polynomials in . This allows exact
enumeration of the moments for small to determine exact formulae for all
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