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Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes [article]

Christian Krattenthaler
2006 arXiv   pre-print
We put recent results by Chen, Deng, Du, Stanley and Yan on crossings and nestings of matchings and set partitions in the larger context of the enumeration of fillings of Ferrers shape on which one imposes  ...  While Chen et al. work with Robinson-Schensted-like insertion/deletion algorithms, we use the growth diagram construction of Fomin to obtain our results.  ...  of squares which belong to the Ferrers diagram of µ but not to the Ferrers diagram of ν.  ... 
arXiv:math/0510676v2 fatcat:xqm4sehgujeabe33yfcgxv6b5i

Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes

C. Krattenthaler
2006 Advances in Applied Mathematics  
We put recent results by Chen, Deng, Du, Stanley and Yan on crossings and nestings of matchings and set partitions in the larger context of the enumeration of fillings of Ferrers shape on which one imposes  ...  While Chen et al. work with Robinson-Schenstedlike insertion/deletion algorithms, we use the growth diagram construction of Fomin to obtain our results.  ...  I would like to thank Anders Björner and Richard Stanley, and the Institut Mittag-Leffler, for giving me the opportunity to work in a relaxed and inspiring atmosphere in the framework of this programme  ... 
doi:10.1016/j.aam.2005.12.006 fatcat:ezn7vxfcsvdtte2wmhodyg2j7u

The citation triad: An overview of a scientist's publication output based on Ferrers diagrams

Fiorenzo Franceschini, Domenico Maisano
2010 Journal of Informetrics  
In a recent work by Anderson et al. (2008) , Ferrers diagrams and Durfee squares are used to represent the scientific output of a scientist and construct a new h-based bibliometric indicator, the tapered  ...  Subsequently, we propose a new bibliometric tool, the citation triad (CT), that better exploits the information contained in a Ferrers diagram, giving a synthetic overview of a scientist's publication  ...  A new bibliometric tool for synthesising Ferrers diagrams Despite our criticism of h T , we give merit to Anderson et al. (2008) for having introduced Ferrers diagrams to represent the scientific output  ... 
doi:10.1016/j.joi.2010.05.004 fatcat:djfdrietmvatfbdchs3txxh6na

Lonesum and Γ-free 0-1 fillings of Ferrers shapes [article]

Gábor V. Nagy, Beáta Bényi
2019 arXiv   pre-print
As an application, we give a new combinatorial interpretation of Genocchi numbers in terms of Callan sequences. Further, we recover some of Hetyei's results on alternating acyclic tournaments.  ...  We show that Γ-free fillings and lonesum fillings of Ferrers shapes are equinumerous by applying a previously defined bijection on matrices for this more general case and by constructing a new bijection  ...  A Γ-free and a non-Γ-free Ferrers diagram In this paper we think of n × k 0-1 matrices as Ferrers diagrams of rectangular shape, namely, Ferrers diagrams corresponding to the partition (k, k, . . . , k  ... 
arXiv:1911.10342v1 fatcat:db7eywo55felvmeob3up4ttami

A Note on Covering Young Diagrams with Applications to Local Dimension of Posets [article]

Stefan Felsner, Torsten Ueckerdt
2019 arXiv   pre-print
We prove that in every cover of a Young diagram with 2kk steps with generalized rectangles there is a row or a column in the diagram that is used by at least k+1 rectangles.  ...  Our results can be rephrased in terms of local covering numbers of difference graphs with complete bipartite graphs, which has applications in the recent notion of local dimension of partially ordered  ...  Ferrers Dimension The aim of this section is to provide some links to research where related things have been investigated with a different terminology. A Ferrers diagram is a Young diagram.  ... 
arXiv:1902.08223v1 fatcat:dnjhn2okdfcn5atfqgxmv3osxu

Page 796 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
;-,- Here, the author considers lattice diagrams which are obtained from Ferrers diagrams « by removing k cells from the “shadow” of some fixed cell (i, 7), where the shadow of cell (i, 7) consists of  ...  all the cells (i’, j’) in the Ferrers diagram with i‘ >i and j’ > j.  ... 

Large Constant Dimension Codes and Lexicodes [article]

Natalia Silberstein, Tuvi Etzion
2010 arXiv   pre-print
Even so, we found that some constant dimension lexicodes are larger than other known codes. We show how to make the computer search more efficient.  ...  In this context we present a formula for the computation of the distance between two subspaces, not necessarily of the same dimension.  ...  We introduce now a variant of the construction of a lexicode with a seed.  ... 
arXiv:1003.4879v1 fatcat:ut2zw4wbz5dwve2mp36ratwb5y

Large constant dimension codes and lexicodes

Natalia Silberstein, Tuvi Etzion
2011 Advances in Mathematics of Communications  
Even so, we found that some constant dimension lexicodes are larger than other known codes. We show how to make the computer search more efficient.  ...  All the codewords in such a code are subspaces of F n q with a given dimension.  ...  We introduce now a variant of the construction of a lexicode with a seed.  ... 
doi:10.3934/amc.2011.5.177 fatcat:ihrsl52emjd2pcemjapccg4ocy

Proposals for evaluating the regularity of a scientist's research output

Fiorenzo Franceschini, Domenico Maisano
2011 Scientometrics  
These tools are respectively (1) the PY/CY diagram, (2) the publication/citation Ferrers diagram and (3) a simplified procedure for comparing the research output of several scientists according to their  ...  Description of these tools is supported by several examples.  ...  The suggested tools have some limitations. They should be used to compare scientists in the same scientific field and with similar career lengths.  ... 
doi:10.1007/s11192-011-0371-4 fatcat:2as43t254zehhh3dtx6ayvv3py

Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$

Jonathan Bloom, Dan Saracino
2012 Discrete Mathematics & Theoretical Computer Science  
In the present paper we provide such a reformulation of $\phi^*$, by modifying the growth diagram algorithm of Fomin.  ...  of taking inverses.  ...  Acknowledgements The first author would like to thank his thesis advisor, Sergi Elizalde, for suggesting the problem of reformulating φ * .  ... 
doi:10.46298/dmtcs.3018 fatcat:hfxafsd7hrcmthfylarvga3ypi

Page 6503 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
We show that assuming hardness of some variants of this MIHNP leads to very efficient algebraic PRNGs and MACs.”  ...  Such a shift register is defined by a unital ideal /< R[x, and a Ferrers diagram Y C Ni. The author presents a class of ideals J which along with Ferrers diagrams define the A-LSFR.  ... 

On Covering Numbers, Young Diagrams, and the Local Dimension of Posets [article]

Gábor Damásdi, Stefan Felsner, António Girão, Balázs Keszegh, David Lewis, Dániel T. Nagy, Torsten Ueckerdt
2020 arXiv   pre-print
We conclude with some remarks on covering numbers for digraphs and Ferrers dimension.  ...  In particular we show that in every cover of a Young diagram with 2kk steps with generalized rectangles there is a row or a column in the diagram that is used by at least k+1 rectangles, and prove that  ...  Acknowledgments This paper has been assembled from drafts of three groups of authors who had independently obtained Theorem 1. The research of Felsner and Ueckerdt has partly been published in [8] .  ... 
arXiv:2001.06367v1 fatcat:ecc7nhpp35eljh7f7mgxnauwui

Combinatorics of the permutation tableaux of type B [article]

Sylvie Corteel, Matthieu Josuat-Vergès, Jang Soo Kim
2012 arXiv   pre-print
There are also some pattern-like statistics arising from variants of the bijection of Fran\ccon and Viennot.  ...  The signed permutation statistics arising here are of several kinds. Firstly, there are several variants of descents and excedances, and more precisely of flag descents and flag excedances.  ...  We thank Philippe Nadeau and Lauren Williams for constructive discussions during the elaboration of this work.  ... 
arXiv:1203.0154v1 fatcat:fqwhuuwxorbh3jt7wmcrbzya5i

Page 699 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
The BK-stratification is used to study the bifurcation diagrams of (transversal) parametrized families of linear systems.  ...  Some possible applications of the canonical form are outlined, including stabilization of systems by feedback.  ... 

On Finite Analogs of Schmidt's Problem and Its Variants [article]

Alexander Berkovich, Ali Kemal Uncu
2022 arXiv   pre-print
We also translate some of our Schmidt's problem alike relations to weighted partition counts with multiplicative weights in relation to Rogers-Ramanujan partitions.  ...  Our new Schmidt type results include the use of even-indexed parts' sums, alternating sum of parts, and hook lengths as well as the odd-indexed parts' sum which appears in the original Schmidt's problem  ...  weighted count of 4-variable decorated Ferrers diagrams.  ... 
arXiv:2205.00527v2 fatcat:lzruikpmpvgo3g53pu22vtvliq
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