2,584 research outputs found
Complementary Algorithms For Tableaux
We study four operations defined on pairs of tableaux. Algorithms for the
first three involve the familiar procedures of jeu de taquin, row insertion,
and column insertion. The fourth operation, hopscotch, is new, although
specialised versions have appeared previously. Like the other three operations,
this new operation may be computed with a set of local rules in a growth
diagram, and it preserves Knuth equivalence class. Each of these four
operations gives rise to an a priori distinct theory of dual equivalence. We
show that these four theories coincide. The four operations are linked via the
involutive tableau operations of complementation and conjugation.Comment: 29 pages, 52 .eps files for figures, JCTA, to appea
The weighted hook length formula
Based on the ideas in [CKP], we introduce the weighted analogue of the
branching rule for the classical hook length formula, and give two proofs of
this result. The first proof is completely bijective, and in a special case
gives a new short combinatorial proof of the hook length formula. Our second
proof is probabilistic, generalizing the (usual) hook walk proof of
Green-Nijenhuis-Wilf, as well as the q-walk of Kerov. Further applications are
also presented.Comment: 14 pages, 4 figure
A New Rational Algorithm for View Updating in Relational Databases
The dynamics of belief and knowledge is one of the major components of any
autonomous system that should be able to incorporate new pieces of information.
In order to apply the rationality result of belief dynamics theory to various
practical problems, it should be generalized in two respects: first it should
allow a certain part of belief to be declared as immutable; and second, the
belief state need not be deductively closed. Such a generalization of belief
dynamics, referred to as base dynamics, is presented in this paper, along with
the concept of a generalized revision algorithm for knowledge bases (Horn or
Horn logic with stratified negation). We show that knowledge base dynamics has
an interesting connection with kernel change via hitting set and abduction. In
this paper, we show how techniques from disjunctive logic programming can be
used for efficient (deductive) database updates. The key idea is to transform
the given database together with the update request into a disjunctive
(datalog) logic program and apply disjunctive techniques (such as minimal model
reasoning) to solve the original update problem. The approach extends and
integrates standard techniques for efficient query answering and integrity
checking. The generation of a hitting set is carried out through a hyper
tableaux calculus and magic set that is focused on the goal of minimality.Comment: arXiv admin note: substantial text overlap with arXiv:1301.515
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