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Algorithmic Combinatorics Based on Slicing Posets
[chapter]

2002
*
Lecture Notes in Computer Science
*

This paper describes a technique

doi:10.1007/3-540-36206-1_16
fatcat:s6jppyk2izbq5kagahv6orf2k4
*based**on*a generalization of Birkhoff's theorem of representation of finite distributive lattices that can be used for solving such problems mechanically and efficiently ... Specifically, we give an efficient (polynomial time)*algorithm*to enumerate, count or detect structures that satisfy B when the total set of structures is large but the set of structures satisfying B is ... Every distributive lattice is a ranked*poset*[17] . Predicates*on*ideals Our technique is crucially*based**on*the notion of predicates*on*the set of ideals. ...##
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Algorithmic combinatorics based on slicing posets

2006
*
Theoretical Computer Science
*

This paper describes a technique

doi:10.1016/j.tcs.2006.03.005
fatcat:nz3ykqvso5hadmca4ih3yzrn5q
*based**on*a generalization of Birkhoff's theorem of representation of finite distributive lattices that can be used for solving such problems mechanically and efficiently ... Specifically, we give an efficient (polynomial time)*algorithm*to enumerate, count or detect structures that satisfy B when the total set of structures is large but the set of structures satisfying B is ... Every distributive lattice is a ranked*poset*[17] . Predicates*on*ideals Our technique is crucially*based**on*the notion of predicates*on*the set of ideals. ...##
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Quantized Dual Graded Graphs

2010
*
Electronic Journal of Combinatorics
*

We construct examples

doi:10.37236/360
fatcat:vyobd5aqnrc6ph4pm2vogs6o6e
*based*upon: the Fibonacci differential*poset*, permutations, standard Young tableau, and plane binary trees. ...*algorithm*. ... These examples are*based**on*various combinatorial objects: the Fibonacci differential*poset*(also called the Young-Fibonacci lattice), permutations, standard Young tableau, and plane binary trees. ...##
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Page 9207 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

[Garg, Vijay Kumar] (1-TX-ELC; Austin, TX)

*Algorithmic**combinatorics**based**on**slicing**posets*. ... The*slicing*results are*based**on*a generalization of Birkhoff’s The- orem of representation of finite distributive lattices. ...##
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Venn Diagrams and Symmetric Chain Decompositions in the Boolean Lattice

2004
*
Electronic Journal of Combinatorics
*

A consequence of the approach is a constructive proof that the quotient

doi:10.37236/1755
fatcat:haleumkp45dgzgkcswvoin53xe
*poset*of ${\cal B}_n$, under the relation "equivalence under rotation", has a symmetric chain decomposition whenever $n$ is prime ... We would like to thank Frank Ruskey for many helpful discussions and for his advice*on*drawing the figures. ... For comments and suggestions*on*an earlier version of this paper we are grateful to several people including Branko Grünbaum, Frank Ruskey, Donald Knuth, and the referees. ...##
###
Quantitative and Algorithmic aspects of Barrier Synchronization in Concurrency

2021
*
Discrete Mathematics & Theoretical Computer Science
*

*Based*

*on*this procedure, we develop a generic

*algorithm*to generate process executions uniformly at random. ... This paper is essentially focusing

*on*the the notion of synchronization from the point of view of

*combinatorics*. ... ISSN 1365-8050 Acknowledgements The authors would like to thank the anonymous referees who provided useful and detailed comments

*on*previous versions of that article. ...

##
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Techniques and applications of computation slicing

2005
*
Distributed computing
*

Nonetheless, for such a predicate, we develop an efficient heuristic

doi:10.1007/s00446-004-0117-0
fatcat:jvg2epwudnggpckknqe45ayroy
*algorithm*for computing an approximate*slice*. ... We prove that the*slice*of a computation is uniquely defined for all predicates. We also present efficient*algorithms*for computing the*slice*for several useful classes of predicates. ... However, the*algorithms**based**on*this approach typically have exponential running time. ...##
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Techniques and Applications of Computation Slicing
[article]

2003
*
arXiv
*
pre-print

We prove that the

arXiv:cs/0303010v1
fatcat:pyc4g423j5girpvh4kzb33rawu
*slice*exists and is uniquely defined for all predicates. We present efficient*slicing**algorithms*for several useful classes of predicates. ... We develop efficient heuristic*algorithms*for computing an approximate*slice*for predicates for which computing the*slice*is otherwise provably intractable. ... However, the*algorithms**based**on*this approach may have exponential running time. ...##
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Page 8149 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

Garg [Vijay Kumar Garg],

*Algorithmic**combinatorics**based**on**slicing**posets*(169- 181); Jens Gramm, Jiong Guo and Rolf Niedermeier, Pattern matching for arc-annotated sequences (182-193); Bernhard Heine ... Prasad Sistla, Formal languages and*algorithms*for similarity*based*re- trieval from sequence databases (324-335); Walter Vogler and Ralf Wollowski, Decomposition in asynchronous circuit design (336-347 ...##
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Cyclage, catabolism, and the affine Hecke algebra

2011
*
Advances in Mathematics
*

This turns out to be closely related to the

doi:10.1016/j.aim.2011.07.006
fatcat:nswsy7dov5fcpkoyut3eh7ubxi
*combinatorics*of the cells of H n worked out by Shi, Lusztig, and Xi, and we state explicit conjectures along these lines. ... Multiplying canonical basis elements by a certain element π ∈ H + n corresponds to rotations of words, and*on*cells corresponds to cocyclage. ... We now relate*combinatorics*of the cellular subquotient R 1 n to the cocyclage*poset**on*standard tableaux. ...##
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Cyclage, catabolism, and the affine Hecke algebra
[article]

2010
*
arXiv
*
pre-print

We conjecture how this filtration relates to the

arXiv:1001.1569v1
fatcat:t52bwxcojrdnde2tdvxgeyqjou
*combinatorics*of the cells of _n worked out by Shi, Lusztig, and Xi. ... Multiplying canonical basis elements by a certain element π∈_n corresponds to rotations of words, and*on*cells corresponds to cocyclage. ... We now relate*combinatorics*of the cellular subquotient R 1 n to the cocyclage*poset**on*standard tableaux. ...##
###
Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings

2008
*
Discrete & Computational Geometry
*

Analyzing infinitesimal expansion of the wavefront consisting of points at constant distance from v

doi:10.1007/s00454-008-9052-3
fatcat:ltrez2irufgupiq63mrjxc4tym
*on*S produces an*algorithmic*method for constructing Voronoi diagrams in each facet, and hence the unfolding ... We characterize the cut locus (the closure of the set of points in S with more than*one*shortest path to v) as a polyhedral complex in terms of Voronoi diagrams*on*facets. ... Topological and Geometric*Combinatorics*(April, 2003) . ...##
###
Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings

2006
*
Discrete & Computational Geometry
*

Analyzing infinitesimal expansion of the wavefront consisting of points at constant distance from v

doi:10.1007/s00454-006-1249-0
fatcat:a3w55ohhmfejjkpg23tlqi4upy
*on*S produces an*algorithmic*method for constructing Voronoi diagrams in each facet, and hence the unfolding ... We characterize the cut locus (the closure of the set of points in S with more than*one*shortest path to v) as a polyhedral complex in terms of Voronoi diagrams*on*facets. ... Topological and Geometric*Combinatorics*(April, 2003) . ...##
###
Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings
[article]

2003
*
arXiv
*
pre-print

Analyzing infinitesimal expansion of the wavefront consisting of points at constant distance from v

arXiv:math/0312253v1
fatcat:7f7enli7sbam7pfzh4w7l6mkwy
*on*S produces an*algorithmic*method for constructing Voronoi diagrams in each facet, and hence the unfolding ... This paper is a study of the interaction between the*combinatorics*of boundaries of convex polytopes in arbitrary dimension and their metric geometry. ... Thus as time progresses, wavefront expansion builds the source*poset*by adding*one*event at a time. The*algorithm*. ...##
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Combinatorial Reciprocity Theorems
[article]

2012
*
arXiv
*
pre-print

A common theme of enumerative

arXiv:1201.2212v1
fatcat:tzbm2preknhmbcbjwoalt6itry
*combinatorics*is formed by counting functions that are polynomials evaluated at positive integers. ... In this expository paper, we focus*on*four families of such counting functions connected to hyperplane arrangements, lattice points in polyhedra, proper colorings of graphs, and P-partitions. ... For more*on*the*combinatorics*of hyperplane arrangements, we recommend the survey article [29] . ...
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