The Hook Graphs of the Symmetric Group

J. S. Frame, G. de B. Robinson, Robert Thrall

Type: Article

Publication Date: 1954-01-01

Citations: 459

DOI: https://doi.org/10.4153/cjm-1954-030-1

Abstract

Each irreducible representation [λ] of the symmetric group S n may be identified by a partition [λ] of n into non-negative integral parts λ 1 ≥ λ 2 ≥ … λ n ≥ 0, of which the first λ' j parts are ≥ j , or by a right (Young) diagram also called [λ], that contains λ i nodes in its ith row and λ' j nodes in its jth column.

Locations

Canadian Journal of Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+	Green vertices and sources of simple modules of the symmetric group labelled by hook partitions	2007	Jürgen Müller René Zimmermann
+	Vertices of simple modules of symmetric groups labelled by hook partitions	2014	Susanne Danz Eugenio Giannelli
+	Vertices of simple modules of symmetric groups labelled by hook partitions	2014	Susanne Danz Eugenio Giannelli
+	Note on hook representations of the symmetric group	2016	Murali K. Srinivasan
+ PDF Chat	Vertices of simple modules of symmetric groups labelled by hook partitions	2014	Susanne Danz Eugenio Giannelli
+	Symmetric and Exterior Squares of Hook Representations	2019	Szabolcs Mészáros János Wolosz
+	Symmetric and Exterior Squares of Hook Representations	2019	Szabolcs Mészáros János Wolosz
+	Representations of symmetric groups with non-trivial determinant	2017	Arvind Ayyer Amritanshu Prasad Steven Spallone
+	Young diagrams and the symmetric group	2024
+ PDF Chat	Star Diagrams and the Symmetric Group	1950	R. A. Staal
+	Representations of the Symmetric Groups and the General Linear Groups, Young Diagrams	2003
+	Representations of the Symmetric Groups and the General Linear Groups, Young Diagrams	2015
+	The commuting graph of the symmetric group Sn	2015	Timothy Woodcock
+	The Irreducible Representations of S n: Young Symmetrizers	2022	Roger Howe
+ PDF Chat	Symmetric group character degrees and hook numbers	2007	David Craven
+	Young's representations of the symmetric group	2000	Alain Lascoux
+	Representations of the Symmetric Group	2001	Bruce E. Sagan
+	REPRESENTATIONS OF THE SYMMETRIC GROUPS	1985
+	Representations of the Symmetric Groups	1972
+	Representations of the Symmetric Groups	1991

Works That Cite This (416)

Action	Title	Year	Authors
+	Limit shapes for random square Young tableaux	2006	Boris Pittel Dan Romik
+ PDF Chat	Roots of Descent Polynomials and an Algebraic Inequality on Hook Lengths	2023	Pakawut Jiradilok Thomas McConville
+ PDF Chat	A bijective proof of the hook-length formula for skew shapes	2017	Matjaž Konvalinka
+ PDF Chat	Tableau stabilization and rectangular tableaux fixed by promotion powers	2020	Connor Ahlbach
+	Tableau posets and the fake degrees of coinvariant algebras	2020	Sara Billey Matjaž Konvalinka Joshua P. Swanson
+	On the largest size of a partition that is both s-core and t-core	2009	Amitabha Tripathi
+	Hook length property of d-complete posets via q-integrals	2018	Jang Soo Kim Meesue Yoo
+	Proof of a conjecture of Morales–Pak–Panova on reverse plane partitions	2019	Peter L. Guo Jack C. D. Zhao Michael X. X. Zhong
+ PDF Chat	The algebra of binary search trees	2005	Florent Hivert Jean-Christophe Novelli Jean‐Yves Thibon
+	Intersecting families of permutations	2011	David Ellis Ehud Friedgut Haran Pilpel

Works Cited by This (7)

Action	Title	Year	Authors
+ PDF Chat	Note on Blocks of Symmetric Groups	1951	Tadasi Nakayama Masaru Osima
+ PDF Chat	On some modular properties of irreducible representations of a symmetric group, I	1940	Tadasi Nakayama
+	On <i>p</i>-quotients and star diagrams of the symmetric group	1953	H. K. Farahat
+ PDF Chat	Modular representations of symmetric groups	1951	D. E. Littlewood
+	On the Representations of the Symmetric Group	1938	G. de B. Robinson
+ PDF Chat	On a Conjecture by J. H. Chung	1952	G. de B. Robinson
+ PDF Chat	Star Diagrams and the Symmetric Group	1950	R. A. Staal