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Full-Text Articles in Mathematics
Non-Simplicial Decompositions Of Betti Diagrams Of Complete Intersections, Courtney Gibbons, Jack Jeffries, Sarah Mayes-Tang, Claudiu Raicu, Branden Stone, Bryan White
Non-Simplicial Decompositions Of Betti Diagrams Of Complete Intersections, Courtney Gibbons, Jack Jeffries, Sarah Mayes-Tang, Claudiu Raicu, Branden Stone, Bryan White
Articles
We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-Soederberg theory. That is, given a Betti diagram, we decompose it into pure diagrams. Relaxing the requirement that the degree sequences in such pure diagrams be totally ordered, we are able to define a multiplication law for Betti diagrams that respects the decomposition and allows us to write a simple expression of the decomposition of the Betti diagram of any complete intersection in terms of the degrees of its minimal generators. In the more traditional sense, the decomposition of complete intersections of codimension at most 3 …
Fixing Numbers Of Graphs And Groups, Courtney Gibbons, Joshua D. Laison
Fixing Numbers Of Graphs And Groups, Courtney Gibbons, Joshua D. Laison
Articles
The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the trivial automorphism of G fixes every vertex in S. The fixing set of a group Γ is the set of all fixing numbers of finite graphs with automorphism group Γ. Several authors have studied the distinguishing number of a graph, the smallest number of labels needed to label G so that the automorphism group of the labeled graph is trivial. The fixing number can be thought of as a variation of the distinguishing number in which every label …