45,629 research outputs found
Replication in critical graphs and the persistence of monomial ideals
Motivated by questions about square-free monomial ideals in polynomial rings,
in 2010 Francisco et al. conjectured that for every positive integer k and
every k-critical (i.e., critically k-chromatic) graph, there is a set of
vertices whose replication produces a (k+1)-critical graph. (The replication of
a set W of vertices of a graph is the operation that adds a copy of each vertex
w in W, one at a time, and connects it to w and all its neighbours.)
We disprove the conjecture by providing an infinite family of
counterexamples. Furthermore, the smallest member of the family answers a
question of Herzog and Hibi concerning the depth functions of square-free
monomial ideals in polynomial rings, and a related question on the persistence
property of such ideals
Using Data in Undergraduate Science Classrooms
Provides pedagogical insight concerning the skill of using data The resource being annotated is: http://www.dlese.org/dds/catalog_DATA-CLASS-000-000-000-007.htm
The Complexity of Kings
A king in a directed graph is a node from which each node in the graph can be
reached via paths of length at most two. There is a broad literature on
tournaments (completely oriented digraphs), and it has been known for more than
half a century that all tournaments have at least one king [Lan53]. Recently,
kings have proven useful in theoretical computer science, in particular in the
study of the complexity of the semifeasible sets [HNP98,HT05] and in the study
of the complexity of reachability problems [Tan01,NT02].
In this paper, we study the complexity of recognizing kings. For each
succinctly specified family of tournaments, the king problem is known to belong
to [HOZZ]. We prove that this bound is optimal: We construct a
succinctly specified tournament family whose king problem is
-complete. It follows easily from our proof approach that the problem
of testing kingship in succinctly specified graphs (which need not be
tournaments) is -complete. We also obtain -completeness
results for k-kings in succinctly specified j-partite tournaments, , and we generalize our main construction to show that -completeness
holds for testing k-kingship in succinctly specified families of tournaments
for all
Primary Sources in K–12 Education: Opportunities for Archives
Recent developments in the field of K–12 (kindergarten through twelfth grade) education have made archival resources essential tools for many teachers. Inquiry-based learning, document-based questions, and high stakes standardized testing have converged to make primary resources an important teaching tool in elementary and secondary education. Teaching and testing K–12 students require analysis of primary documents, so that archival records take their place alongside the test tube and the textbook in many American classrooms. These trends represent an opportunity for archives to expand their patron base, establish contacts in the community, contribute to the vitality of public education in their communities, and cultivate the next generation of archives’ users, donors, and supporters. This paper encourages archivists to consider K–12 students and their teachers when planning programs, digital products, and services
The supports of higher bifurcation currents
Let (f_\lambda) be a holomorphic family of rational mappings of degree d on
the Riemann sphere, with k marked critical points c_1,..., c_k, parameterized
by a complex manifold \Lambda. To this data is associated a closed positive
current T_1\wedge ... \wedge T_k of bidegree (k,k) on \Lambda, aiming to
describe the simultaneous bifurcations of the marked critical points. In this
note we show that the support of this current is accumulated by parameters at
which c_1,..., c_k eventually fall on repelling cycles. Together with results
of Buff, Epstein and Gauthier, this leads to a complete characterization of
Supp(T_1\wedge ... \wedge T_k).Comment: 13 page
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