Related papers: Enumeration of Standard Young Tableaux
This is a survey on permutation classes for the upcoming book Handbook of Enumerative Combinatorics.
Using Symbolic Computation with Maple, we can discover lots of (rigorously-proved!) facts about Standard Young Tableaux, in particular the distribution of the entries in any specific cell, and the sorting probabilities.
In this paper we establish an order statistics model of Young tableaux. Multiple integration over nested simplexes is applied to the enumeration of Young tableaux. A brief proof of Frobenius-Young's and Aitken's formulas is given. Partially…
This paper deals with the distribution of descent number in standard Young tableaux of certain shapes. A simple explicit formula is presented for the number of tableaux of any shape with two rows, with any specified number of descents. For…
A survey written for the upcoming "Handbook of Enumerative Combinatorics".
This is a survey article to appear in the "Handbook on Teichmueller Theory".
We consider two questions of Wilf related to Standard Young Tableaux. We provide a partial answer to one question, and that will lead us to a more general answer to the other question. Our answers are purely combinatorial.
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
This paper completely characterizes the standard Young tableaux that can be reconstructed from their sets or multisets of $1$-minors. In particular, any standard Young tableau with at least $5$ entries can be reconstructed from its set of…
This is a survey of results in the enumeration of lattice paths.
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…
Tables are a powerful and popular tool for organizing and manipulating data. A vast number of tables can be found on the Web, which represents a valuable knowledge resource. The objective of this survey is to synthesize and present two…
The expectation of the descent number of a random Young tableau of a fixed shape is given, and concentration around the mean is shown. This result is generalized to the major index and to other descent functions. The proof combines…
Young tableaux are classical combinatorial objects playing recurring and varied roles in representation theory, algebraic geometry and commutative algebra. This article is a short exposition on Young tableaux, written for the "WHAT IS...?"…
This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…
Unexpected product formulas for the number of standard Young tableaux of certain truncated shapes are found and proved. These include shifted staircase shapes minus a square in the NE corner, rectangular shapes minus a square in the NE…
I survey results about, and recent applications of, Salem numbers.
We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. Andre on the number of up-down permutations. The…
This is a survey paper that also contains some new results. It will appear in the proceedings of the AMS summer research institute on Algebraic Geometry at Santa Cruz.
A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.