92,387 research outputs found
Event-Object Reasoning with Curated Knowledge Bases: Deriving Missing Information
The broader goal of our research is to formulate answers to why and how
questions with respect to knowledge bases, such as AURA. One issue we face when
reasoning with many available knowledge bases is that at times needed
information is missing. Examples of this include partially missing information
about next sub-event, first sub-event, last sub-event, result of an event,
input to an event, destination of an event, and raw material involved in an
event. In many cases one can recover part of the missing knowledge through
reasoning. In this paper we give a formal definition about how such missing
information can be recovered and then give an ASP implementation of it. We then
discuss the implication of this with respect to answering why and how
questions.Comment: 13 page
Combinatorial bases for multilinear parts of free algebras with double compatible brackets
Let X be an ordered alphabet. Lie_2(n) (and P_2(n) respectively) are the
multilinear parts of the free Lie algebra (and the free Poisson algebra
respectively) on X with a pair of compatible Lie brackets. In this paper, we
prove the dimension formulas for these two algebras conjectured by B. Feigin by
constructing bases for Lie_2(n) (and P_2(n)) from combinatorial objects. We
also define a complementary space Eil_2(n) to Lie_2(n), give a pairing between
Lie_2(n) and Eil_2(n), and show that the pairing is perfect.Comment: 38 pages; 10 figure
Biconed graphs, edge-rooted forests, and h-vectors of matroid complexes
A well-known conjecture of Richard Stanley posits that the -vector of the
independence complex of a matroid is a pure -sequence. The
conjecture has been established for various classes but is open for graphic
matroids. A biconed graph is a graph with two specified `coning vertices', such
that every vertex of the graph is connected to at least one coning vertex. The
class of biconed graphs includes coned graphs, Ferrers graphs, and complete
multipartite graphs. We study the -vectors of graphic matroids arising from
biconed graphs, providing a combinatorial interpretation of their entries in
terms of `edge-rooted forests' of the underlying graph. This generalizes
constructions of Kook and Lee who studied the M\"obius coinvariant (the last
nonzero entry of the -vector) of graphic matroids of complete bipartite
graphs. We show that allowing for partially edge-rooted forests gives rise to a
pure multicomplex whose face count recovers the -vector, establishing
Stanley's conjecture for this class of matroids.Comment: 15 pages, 3 figures; V2: added omitted author to metadat
Parking functions, labeled trees and DCJ sorting scenarios
In genome rearrangement theory, one of the elusive questions raised in recent
years is the enumeration of rearrangement scenarios between two genomes. This
problem is related to the uniform generation of rearrangement scenarios, and
the derivation of tests of statistical significance of the properties of these
scenarios. Here we give an exact formula for the number of double-cut-and-join
(DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective
bijections between the set of scenarios that sort a cycle and well studied
combinatorial objects such as parking functions and labeled trees.Comment: 12 pages, 3 figure
The Bergman complex of a matroid and phylogenetic trees
We study the Bergman complex B(M) of a matroid M: a polyhedral complex which
arises in algebraic geometry, but which we describe purely combinatorially. We
prove that a natural subdivision of the Bergman complex of M is a geometric
realization of the order complex of its lattice of flats. In addition, we show
that the Bergman fan B'(K_n) of the graphical matroid of the complete graph K_n
is homeomorphic to the space of phylogenetic trees T_n.Comment: 15 pages, 6 figures. Reorganized paper and updated references. To
appear in J. Combin. Theory Ser.
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