Multiplicity expanded: IR theories, multiplicity, and the potential of trans-disciplinary dialogue

Multiplicity of Resonances Equals Multiplicity of the Scattering Matrix

Extensions of the Multiplicity

The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded k-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several directions. We discuss when these bounds are sharp, find a sharp lower bound in case of not necessarily arithmetically Cohen-Macaulay one-dimensional schemes of 3-s...

Medium-modified average multiplicity and multiplicity fluctuations in jets

The energy evolution of average multiplicities and multiplicity fluctuations in jets produced in heavy-ion collisions is investigated from a toy QCD-inspired model. In this model, we use modified splitting functions accounting for medium-enhanced radiation of gluons by a fast parton which propagates through the quark gluon plasma. The leading contribution of the standard production of soft hadr...

The Multiplicity-polar Theorem

The heart of intersection theory resides in the following situation. Given a purely d-dimensional analytic set X, and subsets V and W intersecting at a point x ∈ X, V and W given by i and j equations respectively where i + j = d, then the correct number of times to count x is the multiplicity of the ideal I in the local ring of X at x, where I is the ideal generated by the equations of V and W....

The Ramsey Multiplicity of K4

With the help of computer algorithms, we improve the lower bound on the Ramsey multiplicity of K4, and thus show that the exact value of it is equal to 9. The Ramsey multiplicity M(G) of a graph G is defined as the smallest number of monochromatic copies ofG in any two-coloring of edges of KR(G), whereR(G) is the Ramsey number of G, i.e. the smallest integer n such that any two-coloring of edge...