Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Composite Fermions And Integer Partitions, Arthur Benjamin, Jennifer Quinn, John Quinn, Arkadiusz Wojs
Composite Fermions And Integer Partitions, Arthur Benjamin, Jennifer Quinn, John Quinn, Arkadiusz Wojs
Jennifer J. Quinn
We utilize the KOH theorem to prove the unimodality of integer partitions with at most a parts, all parts less than or equal to b, that are required to contain either repeated or consecutive parts. We connect this result to an open question in quantum physics relating the number of distinct total angular momentum multiplets of a system of N fermions, each with angular momentum ℓ, to those of a system in which each Fermion has angular momentum ℓ*=ℓ−N+1.
Revisiting Fibonacci And Related Sequences, Arthur Benjamin, Jennifer Quinn
Revisiting Fibonacci And Related Sequences, Arthur Benjamin, Jennifer Quinn
Jennifer J. Quinn
This issue focuses on proving several interesting facts about the Fibonacci Sequence using a combinatorial proof. The aim of Delving Deeper is for teachers to pose and solve novel math problems, expand on mathematical connections, or offer new insights into familiar math concepts. Delving Deeper focuses on mathematics content appealing to secondary school teachers. It provides a forum that allows classroom teachers to share their mathematics from their work with students, their classroom investigations and products, and their other experiences. Delving Deeper is a regular department of Mathematics Teacher.
Strong Chromatic Index Of Subset Graphs, Jennifer Quinn, Arthur Benjamin
Strong Chromatic Index Of Subset Graphs, Jennifer Quinn, Arthur Benjamin
Jennifer J. Quinn
The strong chromatic index of a graph G, denoted sq(G), is the minimum number of parts needed to partition the edges of G into induced matchings. For 0 ≤ k ≤ l ≤ m, the subset graph Sm(k, l) is a bipartite graph whose vertices are the k- and l-subsets of an m element ground set where two vertices are adjacent if and only if one subset is contained in the other. We show that sq(Sm(k, l) ) = m choose l-k and that this number satisfies the strong chromatic index conjecture by Brualdi and Quinn for bipartite graphs. Further, …
The Fermion–Boson Transformation In Fractional Quantum Hall Systems, John Quinn, Arkadiusz Wojs, Jennifer Quinn, Arthur Benjamin
The Fermion–Boson Transformation In Fractional Quantum Hall Systems, John Quinn, Arkadiusz Wojs, Jennifer Quinn, Arthur Benjamin
Jennifer J. Quinn
A Fermion to Boson transformation is accomplished by attaching to each Fermion a single flux quantum oriented opposite to the applied magnetic field. When the mean field approximation is made in the Haldane spherical geometry, the Fermion angular momentum l_F is replaced by l_B - l_F - 1/2(N-1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical if and only if the pseudopotential is "harmonic" in form. However, similar low energy bands of states with Laughlin correlations occur in …