scholarly journals Asymptotics for random Young diagrams when the word length and alphabet size simultaneously grow to infinity

Bernoulli ◽  
2010 ◽  
Vol 16 (2) ◽  
pp. 471-492 ◽  
Author(s):  
Jean-Christophe Breton ◽  
Christian Houdré
Keyword(s):  
Word Length ◽  
Young Diagrams ◽  
Alphabet Size ◽  
Random Young Diagrams

scholarly journals On the Random Young Diagrams and Their Cores

1999 ◽  
Vol 86 (2) ◽  
pp. 245-280 ◽  
Author(s):  
Nathan Lulov ◽  
Boris Pittel
Keyword(s):  
Young Diagrams ◽  
Random Young Diagrams

scholarly journals Counting Finite Languages by Total Word Length

Integers ◽  
2011 ◽  
Vol 11 (6) ◽  
Author(s):  
Stefan Gerhold
Keyword(s):  
Explicit Expression ◽  
Generating Function ◽  
Word Length ◽  
Finite Alphabet ◽  
Alphabet Size ◽  
Total Length ◽  
Large Alphabet ◽  
Finite Language

AbstractWe investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and asymptotics for large alphabet size and large total word length are discussed. Moreover, we derive a Gaussian limit law for the number of words in a random finite language.

scholarly journals Restrictions and Generalizations on Comma-Free Codes

10.37236/114 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Alexander L. Churchill
Keyword(s):  
Word Length ◽  
Coding Theory ◽  
Correspondence Problem ◽  
Major Difficulty ◽  
Alphabet Size ◽  
New Class ◽  
Np Complete

A significant sector of coding theory is that of comma-free coding; that is, codes which can be received without the need of a letter used for word separation. The major difficulty is in finding bounds on the maximum number of comma-free words which can inhabit a dictionary. We introduce a new class called a self-reflective comma-free dictionary and prove a series of bounds on the size of such a dictionary based upon word length and alphabet size. We also introduce other new classes such as self-swappable comma-free codes and comma-free codes in q dimensions and prove preliminary bounds for these classes. Finally, we discuss the implications and applications of combining these original concepts, including their implications for the NP-complete Post Correspondence Problem.

scholarly journals On Kerov polynomials for Jack characters (extended abstract)

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Valentin Féray ◽  
Maciej Dołęga
Keyword(s):  
Symmetric Functions ◽  
Partial Result ◽  
Plancherel Measure ◽  
Jack Polynomials ◽  
Young Diagrams ◽  
Power Sum ◽  
International Audience ◽  
Random Young Diagrams

International audience We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on these objects, suggesting some underlying combinatorics. We give a partial result in this direction, showing that some quantities are polynomials in the Jack parameter $\alpha$ with prescribed degree. Our result has several interesting consequences in various directions. Firstly, we give a new proof of the fact that the coefficients of Jack polynomials expanded in the monomial or power-sum basis depend polynomially in $\alpha$. Secondly, we describe asymptotically the shape of random Young diagrams under some deformation of Plancherel measure.

scholarly journals Random Young Diagrams in a Rectangular Box

2012 ◽  
Vol 12 (4) ◽  
pp. 719-745 ◽  
Author(s):  
Dan Beltoft ◽  
Cédric Boutillier ◽  
Nathanaël Enriquez
Keyword(s):  
Young Diagrams ◽  
Random Young Diagrams

ALMOST WORK-OPTIMAL PRAM EREW DECODERS OF LZ COMPRESSED TEXT

2004 ◽  
Vol 14 (03n04) ◽  
pp. 351-359 ◽  
Author(s):  
SERGIO DE AGOSTINO
Keyword(s):  
Word Length ◽  
Window Size ◽  
Alphabet Size ◽  
Decoding Algorithms ◽  
Parallel Decoding ◽  
Computer Word

We show nearly work-optimal parallel decoding algorithms which run on the PRAM EREW in O ( log n) time with O (n/( log n)1/2) processors for text compressed with LZ1 and LZ2 methods, where n is the length of the output string. We also present pseudo work-optimal PRAM EREW decoders for finite window compression and LZ2 compression requiring logarithmic time with O (dn) work, where d is the window size and the alphabet size respectively. Finally, we observe that PRAM EREW decoders requiring O ( log n) time and O (n/ log n) processors are possible with the non-conservative assumption that the computer word length is O ( log 2 n) bits.

Sign in / Sign up

Export Citation Format

Share Document