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Equivalences Among Relational Expressions with the Union and Difference Operators

Yehoshua Sagiv, Mihalis Yannakakis
1980 Journal of the ACM  
(which are used to represent expressions with only select, project, and join) Furthermore, this method is extended to queries formulated by relatmnal expressions that also contain the difference operator  ...  In this paper we extend the theory of tableaux to all relauonal expressions over select, Permission to  ...  Let ~ be the mapping from the symbols of S~ to those of T~ defined by of tableaux ts an expression t.J,_~ ,, where T~, T2, Tn are tableaux having the same target relation scheme.  ... 
doi:10.1145/322217.322221 fatcat:6c2irgsbwfaiflzs4t453ozil4

Efficient optimization of a class of relational expressions

A. V. Aho, Y. Sagiv, J. D. Ullman
1979 ACM Transactions on Database Systems  
Functional dependencies can be used to imply additional equivalences among tableaux.  ...  Although the optimization problem is NP-complete, a polynomial time algorithm exists to optimize tableaux that correspond to an important subclass of queries.  ...  TABLEAUX In this section we show how to represent the mappings defined by SPJ-expressions by specialized matrices called "tableaux."  ... 
doi:10.1145/320107.320112 fatcat:hzvu3ic6l5bd3ezh5nofcakjee

Equivalences among Relational Expressions

A. V. Aho, Y. Sagiv, J. D. Ullman
1979 SIAM journal on computing (Print)  
Next we introduce "simple tableaux," a subclass of tableau for which we can show the equivalence and optimization problems that were computationally difficult for general tableaux are now tractable.  ...  A matrix, called a tableau, is proposed as a natural representative for the value of an expression. It is shown how tableaux can be made to reflect functional dependencies among attributes.  ...  Tableaux. In this section we show how to represent the mappings defined by relational expressions by specialized matrices called "tableaux".  ... 
doi:10.1137/0208017 fatcat:emu2qnlc7vazfjyrserdevjcxm

A Demazure crystal construction for Schubert polynomials

Sami Assaf, Anne Schilling
2018 Algebraic Combinatorics  
We establish this connection by imposing a Demazure crystal structure on key tableaux, recently introduced by the first author in connection with Demazure characters and Schubert polynomials, and linking  ...  The tableaux for which this occurs are precisely the ones not in the image of the column sorting map. 3.2. Crystal operators on semi-standard key tableaux.  ...  The column sorting map is a well-defined, injective map φ : SSKT(a) → SSYT(λ), where λ is the partition rearrangement of a. Proof.  ... 
doi:10.5802/alco.13 fatcat:aykhykvqnjh3pau6zreuphaev4

Tropical integrable systems and Young tableaux: shape equivalence and Littlewood–Richardson correspondence

Shinsuke Iwao
2018 Journal of Integrable Systems  
We present a new characterization of the shape equivalent class and the Littlewood-Richardson correspondence of Young tableaux in terms of tropical (ultradiscrete) integrable systems.  ...  Obviously, this map is expressed by L-terms.  ...  Moreover, this map is expressed by L-terms.  ... 
doi:10.1093/integr/xyy011 fatcat:w66gp6oihnft5lde4cjfn4rzmq

Young tableaux and longest monotone subsequences: An inequality and a conjecture

A. D. Gordon
1984 Proceedings of the Edinburgh Mathematical Society  
In some cases, it is important to know the value of fi N (j), the number of permutations for which <x N =j.  ...  Much work has been done on the following problem, which is sometimes referred to as Ulam's problem: what is the distribution of <x N [ix N '], the length (i.e. number of terms) of a longest monotone increasing  ...  As an illustration, consider deriving an expression for 0^(^-4,3,1) when all terms to the right of it in Table 1 Provided that one defines the zero correction factors for the diagonal entries (for which  ... 
doi:10.1017/s0013091500022501 fatcat:5pjqminzrzabnkfh4r6dhcq3hy

On standard Young tableaux of bounded height [article]

Marni Mishna
2018 arXiv   pre-print
We survey some recent works on standard Young tableaux of bounded height. We focus on consequences resulting from numerous bijections to lattice walks in Weyl chambers.  ...  Consider the following two maps, which both define bijections. A Dyck path with marked down steps is mapped to a Dyck prefix, by flipping all of the marked down steps into upsteps.  ...  A lattice walk model is defined by a set of allowable steps and a region which confines each walk. A walk is a sequence of steps.  ... 
arXiv:1805.08130v1 fatcat:apeobzrxojec5jkcwumwnu2rs4

Various Representations of the Generalized Kostka Polynomials [chapter]

Anatol N. Kirillov, Anne Schilling, Mark Shimozono
2001 The Andrews Festschrift  
There is a natural qdeformation of the Kostka numbers given by the Kostka polynomials which are formally defined as the connection coefficients between the Schur and the Hall-Littlewood polynomials [24  ...  This multiplicity is equal to the cardinality of the set of column-strict Young tableaux of shape λ and content µ.  ...  The maps which play a central rôle in the proof are the transposition maps on LR tableaux and rigged configurations and a statistic preserving embedding on LR tableaux.  ... 
doi:10.1007/978-3-642-56513-7_10 fatcat:37rcnds6gzgabnmpm72tf62ipq

A computer oriented algorithm for the determination of the dimension and character of a modular irreducible SL(n, K)-module

Marilena Pittaluga, Elisabetta Strickland
1989 Journal of symbolic computation  
The algorithm has been implemented on a computer system, using language p-simp, and has as a starting point a classical result of representation theory, which says that each irreducible representation  ...  Moreover, the so-called "straightening formula" enables an explicit basis to be written for the Schur modules and once this has been achieved one can easily write down the matrix of an integral linear map  ...  We define a Young tableau of shape 2: ill /121 as the polynomial in R which expresses the product I-~ .... , [ij, ijj.  ... 
doi:10.1016/s0747-7171(89)80047-1 fatcat:5p7absgan5aunoxjihcvnotytm

Weak dual equivalence for polynomials [article]

Sami Assaf
2017 arXiv   pre-print
Let w be a permutation for which no element of R(w) is virtual. Then the maps d i on reduced expressions give a stable weak dual equivalence for (R(w), des). Proof.  ...  The maps {d i } are well-defined involutions on SKT(a). Theorem 3 . 24 .F 324 The maps {d i } give a dual equivalence for (SKT(a), Des) consisting of a single equivalence class.  ... 
arXiv:1702.04051v1 fatcat:jqtav5iiofcjdjs6hrv5ui54zu

Data exchange with data-metadata translations

Mauricio A. Hernández, Paolo Papotti, Wang-Chiew Tan
2008 Proceedings of the VLDB Endowment  
naturally extend the traditional value correspondences, to constructs required for the mapping language to specify data-metadata translations, and algorithms required for generating mappings and queries  ...  In particular, the ability to perform data-metadata translations, transformation in which data is converted into metadata or metadata is converted into data, is largely ignored.  ...  The exists clause of the mapping defines four set type or dynamic expressions.  ... 
doi:10.14778/1453856.1453888 fatcat:cvz3pvkhcrfxlbknow6vgn364m

Page 5192 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
The plactification map is defined in Section 3 and some of their properties are given.  ...  The map from reduced words to words is defined by the recurrence y(a) = ro,(p(a)), where 4 is the word obtained from a by removing its first letter r and o,(b) is the word which replaces the subword r*  ... 

On the sign representations for the complex reflection groups G(r, p, n)

Aba Mbirika, Thomas Pietraho, William Silver
2016 Contributions to Algebra and Geometry  
We present a formula for the values of the sign representations of the complex reflection groups G(r,p,n) in terms of its image under a generalized Robinson-Schensted map.  ...  Following [9] and [4] , we define a map from W n to same-shape pairs of r-tuples of standard Young tableaux.  ...  For the classical Weyl groups, all of which appear among the above complex reflection groups, the Möbius function of the Bruhat order can be expressed in terms of the values of the sign representation  ... 
doi:10.1007/s13366-016-0289-3 fatcat:3hzezgr5e5hgzgoywf7ebxfz54

A Flexible Ontology Reasoning Architecture for the Semantic Web

Jeff Pan
2007 IEEE Transactions on Knowledge and Data Engineering  
well-known FaCT DL reasoner, which witnesses the two key flexibility features of our proposed architecture: 1) It allows users to define their own data types and data type predicates based on built-in  ...  Recent research has shown that user-defined data types are very useful for Semantic Web and ontology applications.  ...  Given a tableau we define a mapping which maps the abstract nodes of F to elements of S A and maps data type nodes of F to elements of S D .  ... 
doi:10.1109/tkde.2007.17 fatcat:57fvpd5azrgypdfsbvt5672oge

Clip: a Visual Language for Explicit Schema Mappings

Alessandro Raffio, Daniele Braga, Stefano Ceri, Paolo Papotti, Mauricio A. Hernandez
2008 2008 IEEE 24th International Conference on Data Engineering  
Schema elements are connected with lines, which are interpreted as mappings, i.e. high-level logical expressions capturing the relationship between source and target data-sets; these are compiled into  ...  We describe the transformation semantics associated with our "lines" and how they combine to form mappings that are more expressive than those generated by Clio, a well-known mapping tool.  ...  Mapping language We define the semantics of mappings by means of a querylike notation; in the notation, expressions and terms are defined by e ::= S | x | e.l and t ::= e | F [e]; where S is a schema root  ... 
doi:10.1109/icde.2008.4497411 dblp:conf/icde/RaffioBCPH08 fatcat:u4fr4bdlljdpxcuojkqogseelm
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