Filters








5,002 Hits in 6.2 sec

A lattice path approach to counting partitions with minimum rank t

Alexander Burstein, Sylvie Corteel, Alexander Postnikov, Carla D. Savage
2002 Discrete Mathematics  
In this paper, we give a combinatorial proof via lattice paths of the following result due to Andrews and Bressoud: for t 6 1, the number of partitions of n with all successive ranks at least t is equal  ...  to the number of partitions of n with no part of size 2 − t.  ...  Introduction In this paper, we show how to use a lattice path counting technique to establish a relationship between partitions deÿned by rank conditions and partitions with forbidden part sizes.  ... 
doi:10.1016/s0012-365x(01)00225-4 fatcat:2ue7oddkljgn5hbkvtzbl5df6m

Metrics for Clustering Comparison in Bioinformatics

Giovanni Rossi
2016 Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods  
This yields an exact (rather than heuristic) approach to the consensus partition (combinatorial optimization) problem.  ...  From both theoretical and applicative perspectives, a useful and interesting distance between any two partitions is HD, which counts the number of atoms finer than either one but not both.  ...  The approach allows for generalizations in that the size may be replaced with any alternative orderpreserving lattice function, such as the rank (or the entropy of partitions).  ... 
doi:10.5220/0005707102990308 dblp:conf/icpram/Rossi16a fatcat:6oxbxnrkhjf4nivlewzbxn7ava

Diamond-colored distributive lattices, move-minimizing games, and fundamental Weyl symmetric functions: The type A case [article]

Robert G. Donnelly, Elizabeth A. Donovan, Timothy A. Schroeder
2017 arXiv   pre-print
The objective of this game is to find, if possible, the least number of "domino moves" to get from one partition to another, where a domino move is, with one exception, the addition or removal of a domino-shaped  ...  to as the "type A fundamental lattices."  ...  So, since the rank of a partition is simply the minimum number of moves required to go from the minimum partition to the given partition, the rank of σ is given by ρ(σ) = c i . Example 5.12.  ... 
arXiv:1702.00806v1 fatcat:uc6aldt4kbg6pfjzxa5qompuia

Unimodality and Dyck paths [article]

Luca Ferrari
2012 arXiv   pre-print
We propose an original approach to the problem of rankunimodality for Dyck lattices.  ...  It is based on a well known recursive construction of Dyck paths originally developed in the context of the ECO methodology, which provides a partition of Dyck lattices into saturated chains.  ...  Indeed, this is a special case of the unimodality of Gaussian coefficients (counting integer partitions fitting inside a rectangle with respect to their size), which has been proved in several sources  ... 
arXiv:1207.7295v1 fatcat:7kun5vmlv5gyfb6evmzv3mm2lu

A note on rank complement of rational Dyck paths and conjugation of $(m,n)$-core partitions

Guoce Xin
2017 Journal of Combinatorics  
go below the diagonal; (m, n)-cores are partitions with no hook length equal to m or n.  ...  This leads to: i) a new approach to characterizing n-cores; ii) a simple approach for counting the number of self-conjugate (m, n)-cores; iii) a proof of the equivalence of two conjectured combinatorial  ...  We claim that b < n, so that h is the rank of a lattice If a partition λ is an (m, n) core, then clearly so is its conjugate λ T .  ... 
doi:10.4310/joc.2017.v8.n4.a7 fatcat:kseq55gjuvhdfdv7cynlyfke4i

AlphaSum

K. Selçuk Candan, Huiping Cao, Yan Qi, Maria Luisa Sapino
2009 Proceedings of the 12th International Conference on Extending Database Technology Advances in Database Technology - EDBT '09  
To tackle with the inherent complexity, we rely on the properties of the fuzzy interpretation to further develop a novel ranked set cover based evaluation mechanism (RSC).  ...  We formulate the problem of table summarization with the help of value lattices.  ...  Given a weighted value clustering lattice L, a lattice node vj is a clustering of a lattice node vi, denoted by vi vj, if ∃path p = vi vj in L. We also say that vj covers vi.  ... 
doi:10.1145/1516360.1516373 dblp:conf/edbt/CandanCQS09 fatcat:j245eucyijc2letlapyeq6jjmi

Top-k-size keyword search on tree structured data

Aggeliki Dimitriou, Dimitri Theodoratos, Timos Sellis
2015 Information Systems  
To address performance challenges our algorithms exploit a lattice of the partitions of the keyword set, which empowers a linear time performance.  ...  Recent keyword search approaches return lowest common ancestors (LCAs) of the keyword matches ranked with respect to their relevance to the keyword query.  ...  In our context, every path from the source partition to the sink partition represents a unique way of combining keyword instances to partial LCAs to full LCAs.  ... 
doi:10.1016/j.is.2014.07.002 fatcat:jvocpjzbqrdi7e5mxmwike2c5e

Rank complement of rational Dyck paths and conjugation of (m,n)-core partitions [article]

Guoce Xin
2015 arXiv   pre-print
the diagonal; (m,n)-cores are partitions with no hook length equal to m or n.Anderson established a bijection between (m,n)-Dyck paths and (m,n)-cores.  ...  This leads to: i) a new approach to characterizing n-cores; ii) a simple approach for counting the number of self-conjugate (m,n)-cores; iii) a proof of the equivalence of two conjectured combinatorial  ...  The author is very grateful to Professor Adriano Garsia for inspirations and encouraging conversations.  ... 
arXiv:1504.02075v2 fatcat:f4syi5vyxvarfcdefjs6b7bxvm

Noncrossing partitions

Rodica Simion
2000 Discrete Mathematics  
Without attempting to give an exhaustive account, this article illustrates aspects of enumerative and algebraic combinatorics supported by the lattice of noncrossing partitions, re ecting developments  ...  In a 1972 paper, Germain Kreweras investigated noncrossing partitions under the reÿnement order relation.  ...  to her attention valuable references.  ... 
doi:10.1016/s0012-365x(99)00273-3 fatcat:6qht3p2ygzcypgniitb3wyiveq

Weighted paths between partitions [article]

Giovanni Rossi
2016 arXiv   pre-print
With one exception, all of them obtain as minimum-weight paths in the undirected graph corresponding to the Hasse diagram of the partition lattice.  ...  Secondly, another partition distance known as "variation of information" is seen to correspond to a minimum-weight path with edge weights determined by the entropy of partitions.  ...  The geometric approach adopted here enables to analyze further partition distances obtained by replacing the size with alternative partition functions such as entropy, rank, logical entropy and co-size  ... 
arXiv:1509.01852v2 fatcat:iroivm54jndhnfmotakz2ojjpq

Fourier meets Möbius: fast subset convolution [article]

Andreas Björklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto
2006 arXiv   pre-print
To demonstrate the applicability of fast subset convolution, we present the first O^*(2^k n^2 + n m) algorithm for the minimum Steiner tree problem in graphs with n vertices, k terminals, and m edges with  ...  We also discuss extensions to recent O^*(2^n)-time algorithms for covering and partitioning problems (Björklund and Husfeldt, FOCS 2006; Koivisto, FOCS 2006).  ...  A path joins x 1 to x ℓ+1 . A hypergraph is connected if for all distinct x, y ∈ V there exists a path joining x to y.  ... 
arXiv:cs/0611101v1 fatcat:zvrm7bgjwbew7mw5pocjriqsku

Author index

2002 Discrete Mathematics  
, A., S. Corteel, A. Postnikov and C. D. Savage, A lattice path approach to counting partitions with minimum rank t (1-3) 31-39 Chen, G. and X. Yu, A note on fragile graphs (1-3) 41-43 Chen, G., A.  ...  Schelp, Two-edge colorings of graphs with bounded degree in both , C.W. and D.B. West, A Fibonacci tiling of the plane (1-3) 111-116 Jacobson, M.S., see R.J.  ... 
doi:10.1016/s0012-365x(02)00277-7 fatcat:s5wqhobycrgn3kc2st32twlh4m

Page 3198 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
E.] (1-CA; Berkeley, CA); Savage, Carla D. (1-NCS-C; Raleigh, NC) A lattice path approach to counting partitions with minimum rank /.  ...  Summary: “In this paper, we give a combinatorial proof via lattice paths of the following result due to Andrews and Bressoud: for t <1, the number of partitions of ” with all successive ranks at least  ... 

Fourier meets möbius: fast subset convolution

Andreas Björklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto
2007 Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07  
We present a fast algorithm for the subset convolution problem: given functions f and g defined on the lattice of subsets of an n-element set N , compute their subset convolution f * g, defined for all  ...  A path joins x1 to x ℓ+1 . A hypergraph is connected if for all distinct x, y ∈ V there exists a path joining x to y.  ...  For example, considering a slightly different convolution operation of the form h ′ (S) = X T ⊆N f`T´g`S∆T´, (2) where S∆T = (S \ T ) ∪ (T \ S), the Fourier approach immediately yields an evaluation approach  ... 
doi:10.1145/1250790.1250801 dblp:conf/stoc/BjorklundHKK07 fatcat:hvtaeoesqfdo5hnekpxequsb5e

A Natural Family of Flag Matroids

Anna de Mier
2007 SIAM Journal on Discrete Mathematics  
These flag matroids can also be defined in terms of lattice paths and they provide a generalization of the lattice path matroids of [Bonin et al., JCTA 104 (2003)].  ...  A flag matroid can be viewed as a chain of matroids linked by quotients.  ...  Acknowledgements The author thanks Dominic Welsh for asking a question that suggested this work, and Joseph Bonin and Sergi Elizalde for helpful discussions.  ... 
doi:10.1137/050627873 fatcat:ss7gsbtm5jewnij7xnvjvr76em
« Previous Showing results 1 — 15 out of 5,002 results