A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2010; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A lattice path approach to counting partitions with minimum rank t

2002
*
Discrete Mathematics
*

In this paper, we give

doi:10.1016/s0012-365x(01)00225-4
fatcat:2ue7oddkljgn5hbkvtzbl5df6m
*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. ...##
###
Metrics for Clustering Comparison in Bioinformatics

2016
*
Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods
*

This yields an exact (rather than heuristic)

doi:10.5220/0005707102990308
dblp:conf/icpram/Rossi16a
fatcat:6oxbxnrkhjf4nivlewzbxn7ava
*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*). ...##
###
Diamond-colored distributive lattices, move-minimizing games, and fundamental Weyl symmetric functions: The type A case
[article]

2017
*
arXiv
*
pre-print

The objective of this game is

arXiv:1702.00806v1
fatcat:uc6aldt4kbg6pfjzxa5qompuia
*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. ...##
###
Unimodality and Dyck paths
[article]

2012
*
arXiv
*
pre-print

We propose an original

arXiv:1207.7295v1
fatcat:7kun5vmlv5gyfb6evmzv3mm2lu
*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 ...##
###
A note on rank complement of rational Dyck paths and conjugation of $(m,n)$-core partitions

2017
*
Journal of Combinatorics
*

go below the diagonal; (m, n)-cores are

doi:10.4310/joc.2017.v8.n4.a7
fatcat:kseq55gjuvhdfdv7cynlyfke4i
*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*. ...##
###
AlphaSum

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. ...

##
###
Top-k-size keyword search on tree structured data

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. ...

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

2015
*
arXiv
*
pre-print

the diagonal; (m,n)-cores are

arXiv:1504.02075v2
fatcat:f4syi5vyxvarfcdefjs6b7bxvm
*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. ...##
###
Noncrossing partitions

2000
*
Discrete Mathematics
*

Without attempting

doi:10.1016/s0012-365x(99)00273-3
fatcat:6qht3p2ygzcypgniitb3wyiveq
*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. ...##
###
Weighted paths between partitions
[article]

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 ...

##
###
Fourier meets Möbius: fast subset convolution
[article]

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. ...

##
###
Author index

2002
*
Discrete Mathematics
*

,

doi:10.1016/s0012-365x(02)00277-7
fatcat:s5wqhobycrgn3kc2st32twlh4m
*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. ...##
###
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

2007
*
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07
*

We present

doi:10.1145/1250790.1250801
dblp:conf/stoc/BjorklundHKK07
fatcat:hvtaeoesqfdo5hnekpxequsb5e
*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*...##
###
A Natural Family of Flag Matroids

2007
*
SIAM Journal on Discrete Mathematics
*

These flag matroids can also be defined in terms of

doi:10.1137/050627873
fatcat:ss7gsbtm5jewnij7xnvjvr76em
*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. ...
« Previous

*Showing results 1 — 15 out of 5,002 results*