scholarly journals The Size of the rth Smallest Component in Decomposable Structures with a Restricted Pattern

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Li Dong ◽  
Zhicheng Gao ◽  
Daniel Panario
Keyword(s):  
Asymptotic Expression ◽  
Combinatorial Structure ◽  
International Audience ◽  
Decomposable Structures ◽  
Restricted Pattern

International audience In our previous work [paper1], we derived an asymptotic expression for the probability that a random decomposable combinatorial structure of size n in the \exp -\log class has a given restricted pattern. In this paper, under similar conditions, we provide the probability that a random decomposable combinatorial structure has a given restricted pattern and the size of its rth smallest component is bigger than k, for r,k given integers. Our studies apply to labeled and unlabeled structures. We also give several concrete examples.

scholarly journals Asymptotics of Smallest Component Sizes in Decomposable Combinatorial Structures of Alg-Log Type

2010 ◽  
Vol Vol. 12 no. 2 ◽  
Author(s):  
Li Dong ◽  
Zhicheng Gao ◽  
Daniel Panario ◽  
Bruce Richmond
Keyword(s):  
Generating Function ◽  
Combinatorial Structure ◽  
Asymptotic Estimates ◽  
Asymptotic Results ◽  
Combinatorial Structures ◽  
Combinatorial Objects ◽  
International Audience ◽  
Restricted Pattern

International audience A decomposable combinatorial structure consists of simpler objects called components which by thems elves cannot be further decomposed. We focus on the multi-set construction where the component generating function C(z) is of alg-log type, that is, C(z) behaves like c + d(1 -z/rho)(alpha) (ln1/1-z/rho)(beta) (1 + o(1)) when z is near the dominant singularity rho. We provide asymptotic results about the size of thes mallest components in random combinatorial structures for the cases 0 < alpha < 1 and any beta, and alpha < 0 and beta=0. The particular case alpha=0 and beta=1, the so-called exp-log class, has been treated in previous papers. We also provide similar asymptotic estimates for combinatorial objects with a restricted pattern, that is, when part of its factorization patterns is known. We extend our results to include certain type of integers partitions. partitions

scholarly journals Asymptotics of Decomposable Combinatorial Structures of Alg-Log Type With Positive Log Exponent

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Zhicheng Gao ◽  
David Laferrière ◽  
Daniel Panario
Keyword(s):  
Generating Function ◽  
Asymptotic Results ◽  
Combinatorial Structures ◽  
International Audience ◽  
Decomposable Structures

International audience We consider the multiset construction of decomposable structures with component generating function $C(z)$ of alg-log type, $\textit{i.e.}$, $C(z) = (1-z)^{-\alpha} (\log \frac{1}{ 1-z})^{\beta}$. We provide asymptotic results for the number of labeled objects of size $n$ in the case when $\alpha$ is positive and $\beta$ is positive and in the case $\alpha = 0$ and $\beta \geq 2$. The case $0<-\alpha <1$ and any $\beta$ and the case $\alpha > 0$ and $\beta = 0$ have been treated in previous papers. Our results extend previous work of Wright.

scholarly journals Optimal Prefix and Suffix Queries on Texts

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Maxime Crochemore ◽  
Costas S. Iliopoulos ◽  
M. Sohel Rahman
Keyword(s):  
Data Structure ◽  
Suffix Tree ◽  
Query Time ◽  
Time And Space ◽  
Matching Problem ◽  
International Audience ◽  
Tree Data ◽  
Tree Data Structure ◽  
Restricted Pattern ◽  
Time And Space Complexity

International audience In this paper, we study a restricted version of the position restricted pattern matching problem introduced and studied by Mäkinen and Navarro [Position-Restricted Substring Searching, LATIN 2006]. In the problem handled in this paper, we are interested in those occurrences of the pattern that lies in a suffix or in a prefix of the given text. We achieve optimal query time for our problem against a data structure which is an extension of the classic suffix tree data structure. The time and space complexity of the data structure is dominated by that of the suffix tree. Notably, the (best) algorithm by Mäkinen and Navarro, if applied to our problem, gives sub-optimal query time and the corresponding data structure also requires more time and space.

scholarly journals Tropical Ideals

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Diane Maclagan ◽  
Felipe Rincón
Keyword(s):  
Special Class ◽  
Tropical Geometry ◽  
Combinatorial Structure ◽  
International Audience ◽  
Algebraic Foundation

International audience We introduce and study a special class of ideals over the semiring of tropical polynomials, which we calltropical ideals, with the goal of developing a useful and solid algebraic foundation for tropical geometry. We exploretheir rich combinatorial structure, and prove that they satisfy numerous properties analogous to classical ideals.

scholarly journals Total positivity for the Lagrangian Grassmannian

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Rachel Karpman
Keyword(s):  
Symplectic Form ◽  
Total Positivity ◽  
Combinatorial Structure ◽  
Schubert Varieties ◽  
Flag Varieties ◽  
Young Diagrams ◽  
Lagrangian Grassmannian ◽  
Planar Network ◽  
International Audience ◽  
Isotropic Subspaces

International audience The positroid decomposition of the Grassmannian refines the well-known Schubert decomposition, and has a rich combinatorial structure. There are a number of interesting combinatorial posets which index positroid varieties,just as Young diagrams index Schubert varieties. In addition, Postnikov’s boundary measurement map gives a family of parametrizations for each positroid variety. The domain of each parametrization is the space of edge weights of a weighted planar network. The positroid stratification of the Grassmannian provides an elementary example of Lusztig’s theory of total non negativity for partial flag varieties, and has remarkable applications to particle physics.We generalize the combinatorics of positroid varieties to the Lagrangian Grassmannian, the moduli space of maximal isotropic subspaces with respect to a symplectic form

scholarly journals The Degree Distribution of Thickened Trees

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Michael Drmota ◽  
Bernhard Gittenberger ◽  
Alois Panholzer
Keyword(s):  
Power Law ◽  
Real World ◽  
Degree Distribution ◽  
Combinatorial Structure ◽  
Random Real ◽  
Asymptotic Power ◽  
Scale Free ◽  
International Audience ◽  
Recursive Trees

International audience We develop a combinatorial structure to serve as model of random real world networks. Starting with plane oriented recursive trees we substitute the nodes by more complex graphs. In such a way we obtain graphs having a global tree-like structure while locally looking clustered. This fits with observations obtained from real-world networks. In particular we show that the resulting graphs are scale-free, that is, the degree distribution has an asymptotic power law.

scholarly journals A lattice on decreasing trees : the metasylvester lattice

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Viviane Pons
Keyword(s):  
Combinatorial Structure ◽  
Combinatorial Properties ◽  
Tamari Lattice ◽  
Nous Montrons ◽  
International Audience ◽  
Tamari Lattices ◽  
Labelled Trees

International audience We introduce a new combinatorial structure: the metasylvester lattice on decreasing trees. It appears in the context of the $m$-Tamari lattices and other related $m$-generalizations. The metasylvester congruence has been recently introduced by Novelli and Thibon. We show that it defines a sublattice of the $m$-permutations where elements can be represented by decreasing labelled trees: the metasylvester lattice. We study the combinatorial properties of this new structure. In particular, we give different realizations of the lattice. The $m$-Tamari lattice is by definition a sublattice of our newly defined metasylvester lattice. It leads us to a new realization of the $m$-Tamari lattice, using certain chains of the classical Tamari lattice. Nous définissons une nouvelle structure combinatoire : le treillis métasylvestre sur les arbres décroissants. Il apparaît dans le contexte des treillis $m$-Tamari et des autres $m$-généralisations. La congruence métasylvestre a été introduite récemment par Novelli et Thibon. Nous montrons qu’elle définit un sous-treillis du treillis sur les $m$-permutations où les éléments sont représentés par des arbres étiquetés décroissants : le treillis métasylvestre. Nous étudions les propriétés combinatoires de ce treillis ainsi que des classes métasylvestres. En particulier, nous en donnons plusieurs réalisations. Le treillis de $m$-Tamari est par définition un sous-treillis du treillis métasylvestre. Cela nous amène à une nouvelle réalisation du treillis de$m$-Tamari par des chaines du treillis de Tamari classiques.

scholarly journals Branching rules in the ring of superclass functions of unipotent upper-triangular matrices

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Nathaniel Thiem
Keyword(s):  
Symmetric Functions ◽  
Combinatorial Structure ◽  
Classical Representation ◽  
Set Partitions ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Branching Rules ◽  
International Audience ◽  
Structure Constants ◽  
Supercharacter Theory

International audience It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical representation theory of the symmetric group. This paper begins by exploring a connection to the ring of symmetric functions in non-commuting variables that mirrors the symmetric group's relationship with the ring of symmetric functions. It then also investigates some of the representation theoretic structure constants arising from the restriction, tensor products and superinduction of supercharacters.

Somethin’ about Scandinavia: Danish Shorts on the Post-war International Scene

2018 ◽  
Author(s):  
C. Claire Thomson
Keyword(s):  
United Nations ◽  
International Collaboration ◽  
Marshall Plan ◽  
The Third ◽  
Animated Film ◽  
International Audience ◽  
Post War ◽  
Nordic Cooperation

Building on the picture of post-war Anglo-Danish documentary collaboration established in the previous chapter, this chapter examines three cases of international collaboration in which Dansk Kulturfilm and Ministeriernes Filmudvalg were involved in the late 1940s and 1950s. They Guide You Across (Ingolf Boisen, 1949) was commissioned to showcase Scandinavian cooperation in the realm of aviation (SAS) and was adopted by the newly-established United Nations Film Board. The complexities of this film’s production, funding and distribution are illustrative of the activities of the UN Film Board in its first years of operation. The second case study considers Alle mine Skibe (All My Ships, Theodor Christensen, 1951) as an example of a film commissioned and funded under the auspices of the Marshall Plan. This US initiative sponsored informational films across Europe, emphasising national solutions to post-war reconstruction. The third case study, Bent Barfod’s animated film Noget om Norden (Somethin’ about Scandinavia, 1956) explains Nordic cooperation for an international audience, but ironically exposed some gaps in inter-Nordic collaboration in the realm of film.

Conclusion

2018 ◽  
Author(s):  
Alistair Fox
Keyword(s):  
National Identity ◽  
New Zealand ◽  
Identity Formation ◽  
Essential Role ◽  
Coming Of Age ◽  
Financial Returns ◽  
Self Recognition ◽  
International Audience ◽  
National Identity Formation

The conclusion reaffirms the essential role played by cinema generally, and the coming-of-age genre in particular, in the process of national identity formation, because of its effectiveness in facilitating self-recognition and self-experience through a process of triangulation made possible, for the most part, by a dialogue with some of the nation’s most iconic works of literature. This section concludes by point out the danger posed, however, by an observable trend toward generic standardization in New Zealand films motivated by a desire to appeal to an international audience out of consideration for the financial returns expected by funding bodies under current regimes.

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