Filters








704 Hits in 6.0 sec

Enumeration of generalized Young tableaux with bounded height

Seul Hee Choi, Dominique Gouyou-Beauchamps
1993 Theoretical Computer Science  
Gouyou-Beauchamps, Enumeration of generalized Young tableaux with bounded height, Theoretical Computer Science 117 (1993) 137-151.  ...  We show that the number of such tableaux with entries between 1 and n, with p columns having an odd number of elements and having at most 2k rows, is the product The proof is mainly bijective, using configurations  ...  Fig. 1 . 1 Desainte-Catherine and Viennot [3] proved a companion formula for the number b n,2k of generalized Young tableaux with columns having only an even number of elements and bounded by height q  ... 
doi:10.1016/0304-3975(93)90309-h fatcat:434llgwi2nf2xkrm4iikc3bwdy

On standard Young tableaux of bounded height [article]

Marni Mishna
2018 arXiv   pre-print
We survey some recent works on standard Young tableaux of bounded height. We focus on consequences resulting from numerous bijections to lattice walks in Weyl chambers.  ...  I am grateful for the patience and wisdom of the anonymous referees. The author's research is also partially funded by NSERC Discovery Grant RGPIN-04157.  ...  In this work we are interested in the number of standard Young tableaux of a given size with the height is bounded by a fixed value. 1.1. Enumeration formulas.  ... 
arXiv:1805.08130v1 fatcat:apeobzrxojec5jkcwumwnu2rs4

A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape

Sophie Burrill, Stephen Melczer, Marni Mishna
2015 Discrete Mathematics & Theoretical Computer Science  
Oscillating tableau of height bounded by $k$ ending in a row are in bijection with Young tableaux of bounded height 2$k$. We discuss this recent result, and somegenerating function implications.  ...  First, we prove that hesitating tableaux of height at most two ending with a row shape are counted by Baxter numbers.  ...  , the hyperbolic Bessel function of the first kind of order j. Let theỸ k (t) be the exponential generating function for the class of standard Young tableaux with height bounded by k.  ... 
doi:10.46298/dmtcs.2530 fatcat:negcv2tuzfenxowzwsdzjrncvu

A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape [article]

Sophie Burrill, Stephen Melczer, Marni Mishna
2015 arXiv   pre-print
We then conjecture that oscillating tableau of height bounded by k ending in a row are in bijection with Young tableaux of bounded height 2k.  ...  First, we prove that hesitating tableaux of height at most two ending with a row shape are counted by Baxter numbers.  ...  , the hyperbolic Bessel function of the first kind of order j. Let the Ỹk (t) be the exponential generating function for the class of standard Young tableaux with height bounded by k.  ... 
arXiv:1411.6606v2 fatcat:ria5rhxl7bgx7ikc5vckcwurza

Tableau sequences, open diagrams, and Baxter families

Sophie Burrill, Julien Courtiel, Eric Fusy, Stephen Melczer, Marni Mishna
2016 European journal of combinatorics (Print)  
Remarkably two subclasses of open diagrams are equinumerous with well known objects: standard Young tableaux of bounded height, and Baxter permutations.  ...  We show that walks that start at ∅, end at a row shape, and only visit partitions of bounded height are in bijection with a new type of arc diagram -- open diagrams.  ...  The work of MM is partially supported by an NSERC Discovery Grant.  ... 
doi:10.1016/j.ejc.2016.05.011 fatcat:7ewn6ibhizef7ctmnjldciqbeu

Enumerating quasi-Yamanouchi tableaux of Durfee size two [article]

George Wang
2018 arXiv   pre-print
They are a subset of semistandard Young tableaux that are also a refinement on standard Young tableaux, and they can be used to improve the fundamental quasisymmetric expansion of Schur polynomials.  ...  We prove a product formula for enumerating certain quasi-Yamanouchi tableaux and provide strong evidence that no product formula exists in general for other shapes.  ...  For example, Frame, Robinson, and Thrall produced the celebrated hook-length formula that counts standard Young tableaux of a given shape [FRT54] , and Stanley enumerated semistandard Young tableaux with  ... 
arXiv:1610.04206v2 fatcat:mj34h7hr4zbelerxgy6u6glomu

Conjectures on the enumeration of tableaux of bounded height

François Bergeron, Luc Favreau, Daniel Krob
1995 Discrete Mathematics  
We express general conjectures for the explicit form of P-recurrences for the number of Young standard tablaux of height bounded by h.  ...  These recurrences are shown to be compatible with known results and Regev's asymptotic evaluations.  ...  Acknowledgements The Maple package 9fun (available as a shared library) was used extensively in the elaboration of the conjectures in this note.  ... 
doi:10.1016/0012-365x(94)00148-c fatcat:wbd32fle4vgzpodufkg2ycknqi

Three-dimensional Catalan numbers and product-coproduct prographs [article]

Nicolas Borie
2017 arXiv   pre-print
We present some combinatorial bijections positioning product-coproduct prographs as key objects to probe families of objects enumerated by the 3-dimensional Catalan numbers.  ...  We show that such graphs are enumerated by the 3-dimensional Catalan numbers.  ...  Although it is complicated to describe in general, the Schützenberger involution of rectangular standard Young tableaux can be obtained with an easy algorithm.  ... 
arXiv:1704.00212v1 fatcat:rcstq3akcvafhjyykld4pish4q

Generating Functions for Inverted Semistandard Young Tableaux and Generalized Ballot Numbers [article]

Paul Drube
2016 arXiv   pre-print
For m-row shapes λ and standard content μ, the total number of k-inverted standard Young tableau of shape λ are then enumerated by relating such tableaux to m-dimensional generalizations of Dyck paths  ...  Our various results are then used to directly enumerate all k-inverted semistandard Young tableaux with arbitrary content and two-row shape λ = a^1 b^1, as well as all k-inverted standard Young tableaux  ...  Theorem 4.2 explicitly enumerates k-inverted semistandard Young tableaux for an arbitrary two-row shape λ = a 1 b 1 , generalizing earlier enumerations [5, 3] of two-row inverted tableaux in the standard  ... 
arXiv:1606.04869v1 fatcat:zudd6y2z5fft5ddyl34zfkx34e

Page 5057 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
Bressoud, Definite integral evaluation by enumeration, partial results in the Macdonald conjectures (pp. 48-57); Myriam de Sainte-Catherine and Gérard Viennot, Enumeration of certain Young tableaux with  ...  Gessel, Counting three-line Latin rectangles (pp. 106-111); Dominique Gouyou-Beauchamps, Chemins sous-diagonaux et tableaux de Young [Subdiagonal paths and Young tableaux] (pp. 112-125); André Joyal, Foncteurs  ... 

Counting lattice paths in restricted planes

Seulhee Choi
2000 Discrete Mathematics  
The proofs are purely combinatorial, using the bijections, the technique of the enumeration of noncrossing paths and the re ection principle.  ...  The number of lattice paths of ÿxed length consisting of unit steps in the north, south, east or west directions in the plane {(x; y) ∈ R 2 | 06y6x} is shown.  ...  standard Young tableaux with height bounded by 4, having 2n cells, and 2n+1 p=0 |S 2n+1;p;0 | = C n+1 C n+1 is equal to the number of standard Young tableaux with height bounded by 4, having 2n + 1 cells  ... 
doi:10.1016/s0012-365x(99)00287-3 fatcat:s3srgw4ntvaffooxvjigqaj2qu

Page 3281 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
Summary: “We express general conjectures for the explicit form of P-recurrences for the number of Young standard tableaux of height bounded by h.  ...  of tableaux of bounded height.  ... 

Page 649 of Mathematical Reviews Vol. , Issue 89B [page]

1989 Mathematical Reviews  
Joseph Kung (1-NTXS) 89b:05018 O5A15 OSA10 I15A15 de Sainte-Catherine, Myriam (F-BORD); Viennot, Gérard (F-BORD) Enumeration of certain Young tableaux with bounded height.  ...  The authors consider Young tableaux with entries from {1,2,---,} satisfying: there are at most 2k rows; the rows are strictly increas- ing; the columns are nondecreasing; every column has an even number  ... 

Bounded Height Interlaced Pairs of Parking Functions [article]

Francois Bergeron
2015 arXiv   pre-print
We enumerate interlaced pairs of parking functions whose underlying Dyck path has a bounded height.  ...  We obtain an explicit formula for this enumeration in the form of a quotient of analogs of Chebicheff polynomials having coefficients in the ring of symmetric functions.  ...  With an adequately defined notion of height, our considerations of bounded height may be extended to this more general framework.  ... 
arXiv:1504.07136v1 fatcat:qkxfsc2r6ret3oydz4imgl3aky

Bijections for walks ending on an axis, using open arc diagrams

Julien Courtiel, Éric Fusy, Mathias Lepoutre, Marni Misna
2017 Electronic Notes in Discrete Mathematics  
One consequence is a set of new bijections for standard Young tableaux of bounded height.  ...  Our strategy for simple walks extends to any dimension and yields a new bijective connection between standard Young tableaux of height at most 2k and certain walks with prescribed endpoints in the k-dimensional  ...  [20] for the generating function of standard Young tableaux of even-bounded height.  ... 
doi:10.1016/j.endm.2017.06.052 fatcat:6zifcxqjbnacdp76rvfhxhgk2i
« Previous Showing results 1 — 15 out of 704 results