Hook formula and related identities

1992 ◽  
Vol 59 (5) ◽  
pp. 1029-1040 ◽  
Author(s):  
A. M. Vershik
Keyword(s):  
Hook Formula

Flag manifolds and the hook formula

1980 ◽  
Vol 170 (2) ◽  
pp. 105-107 ◽  
Author(s):  
Howard L. Hiller
Keyword(s):  
Flag Manifolds ◽  
Hook Formula

scholarly journals Skew hook formula for $d$-complete posets via equivariant $K$-theory

2019 ◽  
Vol 2 (4) ◽  
pp. 541-571
Author(s):  
Hiroshi Naruse ◽  
Soichi Okada
Keyword(s):  
Hook Formula ◽  
K Theory

scholarly journals An edge-weighted hook formula for labelled trees

2014 ◽  
Vol 5 (2) ◽  
pp. 245-269
Author(s):  
Valentin Féray ◽  
I. P. Goulden ◽  
Alain Lascoux
Keyword(s):  
Hook Formula ◽  
Labelled Trees

scholarly journals An algorithm which generates linear extensions for a generalized Young diagram with uniform probability

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Kento Nakada ◽  
Shuji Okamura
Keyword(s):  
Young Diagram ◽  
Linear Extensions ◽  
Reduced Decompositions ◽  
Uniform Probability ◽  
Hook Formula ◽  
International Audience

International audience The purpose of this paper is to present an algorithm which generates linear extensions for a generalized Young diagram, in the sense of D. Peterson and R. A. Proctor, with uniform probability. This gives a proof of a D. Peterson's hook formula for the number of reduced decompositions of a given minuscule elements. \par Le but de ce papier est présenter un algorithme qui produit des extensions linéaires pour un Young diagramme généralisé dans le sens de D. Peterson et R. A. Proctor, avec probabilité constante. Cela donne une preuve de la hook formule d'un D. Peterson pour le nombre de décompositions réduites d'un éléments minuscules donné.

scholarly journals A multivariate “inv” hook formula for forests

2012 ◽  
Vol 31 (1-2) ◽  
pp. 33-51 ◽  
Author(s):  
Florent Hivert ◽  
Victor Reiner
Keyword(s):  
Hook Formula

scholarly journals A multivariate hook formula for labelled trees

2013 ◽  
Vol 120 (4) ◽  
pp. 944-959 ◽  
Author(s):  
Valentin Féray ◽  
I.P. Goulden
Keyword(s):  
Hook Formula ◽  
Labelled Trees

Life-cycles of helminth parasites using Gammarus lacustris as an intermediate host in a Canadian lake

Parasitology ◽  
1969 ◽  
Vol 59 (4) ◽  
pp. 795-827 ◽  
Author(s):  
M. Denny
Keyword(s):  
Intermediate Host ◽  
Local Population ◽  
Eutrophic Lake ◽  
Life Cycles ◽  
Helminth Parasites ◽  
New Host ◽  
Gammarus Lacustris ◽  
Hook Formula ◽  
First Time ◽  
New Host Records

The systematics and life-cycles of the helminths of a local population of Gammarus lacustris in a eutrophic lake near Edmonton, Alberta, is reported as part of a larger study of the composition and seasonal dynamics of the helminth fauna of gammarids.A total of 12 species of helminths, including eight cestodes, one nematode and three acanthocephalans, were recovered. Of these, eleven were new host records, ten were assigned to an intermediate host species for the first time, and one, Hymenolepis albertensis sp.nov., was described for the first time.Adults of all twelve helminths were raised in experimentally infested birds and the life-cycles of five species (Lateriporus clerci, L. skrjabini, Hymenolepis albertensis sp.nov., Fimbriaria fasciolaris and Polymorphus marilis) were completed in the laboratory. The larvae are described, and the developmental period in the gammarids, prepatent period and life span of the adults are given for many of the helminths.The rate of development of the cysticercoids of Lateriporus skrjabini was shown to be directly related to the size of the gammarid and inversely related to the intensity of infestation.The proboscis-hook formula was not a good diagnostic character for the separation of the three acanthocephalans, Polymorphus contortus, P. marilis and P. paradoxus; however, the size of the largest hook and the structure of the cystacanth body-wall were good diagnostic characters.I am indebted to Dr J. C. Holmes for advice and encouragement at all stages of the study. I also wish to thank Drs S. Prudhoe and D. R. R. Burt for their editorial assistance, Mr L. Graham for many helpful suggestions and information on the natural definitive hosts of the species encountered, Mr R. Podesta for his laboratory assistance, and Miss E. D. Senio for caring for the ducklings during their first few days of life. The study was supported by the Francis F. Reeve Foundation Graduate Bursary, the Queen Elizabeth Education Scholarship Fund, by the Department of Zoology through a Teaching Assistantship, by a grant from the R. B. Miller Biological Station Fund and by an N.R.C. operating grant (A–1464) to Dr J. C. Holmes.

scholarly journals Asymptotics of Young Diagrams and Hook Numbers

10.37236/1307 ◽  
1997 ◽  
Vol 4 (1) ◽  
Author(s):  
Amitai Regev ◽  
Anatoly Vershik
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Methods ◽  
Symmetric Groups ◽  
Schur Functions ◽  
Young Diagrams ◽  
Arithmetic Properties ◽  
Hook Formula ◽  
Hook Numbers

Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\mu$, we deduce several skew diagrams which are related to $\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know "finite", nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.

scholarly journals An Elementary Proof of the Hook Formula

10.37236/769 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Jason Bandlow
Keyword(s):  
Fundamental Theorem ◽  
Elementary Proof ◽  
Young Tableaux ◽  
Hook Length ◽  
Inductive Approach ◽  
Fundamental Theorem Of Algebra ◽  
Hook Formula

The hook-length formula is a well known result expressing the number of standard tableaux of shape $\lambda$ in terms of the lengths of the hooks in the diagram of $\lambda$. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing more than the fundamental theorem of algebra. This proof was suggested by a $q,t$-analog of the hook formula given by Garsia and Tesler, and is roughly based on the inductive approach of Greene, Nijenhuis and Wilf. We also prove the hook formula in the case of shifted Young tableaux using the same technique.

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