Discrete Mathematics and Combinatorics Commons^™

Generating Sequences Of Clique-Symmetric Graphs Via Eulerian Digraphs, John P. Mcsorley, Thomas D. Porter

Articles and Preprints

Let {G_p1,G_p2, . . .} be an infinite sequence of graphs with G_pn having pn vertices. This sequence is called K_p-removable if G_p1 ≅ K_p, and G_pn − S ≅ G_p(n−1) for every n ≥ 2 and every vertex subset S of G_pn that induces a K_p. Each graph in such a sequence has a high degree of symmetry: every way of removing the vertices of any fixed number of disjoint K_p’s yields the same …

Bounding The Firing Synchronization Problem On A Ring, André Berthiaume, Todd Bittner, Ljubomir Perković, Amber Settle, Janos Simon

Amber Settle

Two New Criteria For Comparison In The Bruhat Order, Brian Drake, Sean Gerrish, Mark Skandera

Dartmouth Scholarship

We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type $A$). One criterion utilizes totally nonnegative polynomials and the other utilizes Schur functions.

On Classifying Finite Edge Colored Graphs With Two Transitive Automorphism Groups, Thomas Q. Sibley

Mathematics Faculty Publications

This paper classifies all finite edge colored graphs with doubly transitive automorphism groups. This result generalizes the classification of doubly transitive balanced incomplete block designs with λ=1 and doubly transitive one-factorizations of complete graphs. It also provides a classification of all doubly transitive symmetric association schemes.

A Theorem On Divergence In The General Sense For Continued Fractions, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

If the odd and even parts of a continued fraction converge to different values, the continued fraction may or may not converge in the general sense. We prove a theorem which settles the question of general convergence for a wide class of such continued fractions. We apply this theorem to two general classes of q continued fraction to show, that if G(q) is one of these continued fractions and |q| > 1, then either G(q) converges or does not converge in the general sense. We also show that if the odd and even parts of the continued fraction K∞n=1an/1 converge to …

On The Divergence Of The Rogers-Ramanujan Continued Fraction On The Unit Circle, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

This paper is an intensive study of the convergence of the Rogers-Ramanujan continued fraction. Let the continued fraction expansion of any irrational number t ∈ (0, 1) be denoted by [0, a1(t), a2(t), · · · ] and let the i-th convergent of this continued fraction expansion be denoted by ci(t)/di(t). Let S = {t ∈ (0, 1) : ai+1(t) ≥ φ di(t) infinitely often}, where φ = (√ 5 + 1)/2. Let YS = {exp(2πit) : t ∈ S}. It is shown that if y ∈ YS then the Rogers-Ramanujan continued fraction, R(y), diverges at y. S is an …

Tree Diagrams For String Links Ii: Determining Chord Diagrams, Blake Mellor

Mathematics Faculty Works

In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term relations).