Chromatic symmetric functions and combinatorial polynomials are central constructs in modern algebraic combinatorics, extending classical graph invariants into rich algebraic frameworks. Originating ...

This jingle has helped generations of algebra students recall the quadratic formula that solves every equation of the form $latex ax^2+bx+c=0$. The formula is as ...

The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. Find the equation of the line of symmetry and ...

This video gives you the fastest and easiest method to understand and sketch parabolas—no complex math required. We break it down step-by-step: finding the vertex, identifying the axis of symmetry, ...

Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).

This paper provides proof of conjectures about the expected values of the jth elementary symmetric function of the roots (i.e. $E(\operatorname{tr}_j A)$) of a non ...