Q-Rook placements and Jordan forms of upper-triangular nilpotent matrices

Martha Yip

Q-Rook placements and Jordan forms of upper-triangular nilpotent matrices

Martha Yip

Mathematics

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

The set of n by n upper-triangular nilpotent matrices with entries in a finite field F_q has Jordan canonical forms indexed by partitions λ ⊢ n. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number F_λ (q) of matrices of fixed Jordan type as a weighted sum over rook placements.

Original language	English
Pages (from-to)	1017-1028
Number of pages	12
Journal	Discrete Mathematics and Theoretical Computer Science
State	Published - 2013
Event	25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France Duration: Jun 24 2013 → Jun 28 2013

Keywords

Jordan canonical form
Nilpotent matrices
Q-rook placements
Set partitions

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Discrete Mathematics and Combinatorics

Cite this

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title = "Q-Rook placements and Jordan forms of upper-triangular nilpotent matrices",

abstract = "The set of n by n upper-triangular nilpotent matrices with entries in a finite field Fq has Jordan canonical forms indexed by partitions λ ⊢ n. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number Fλ (q) of matrices of fixed Jordan type as a weighted sum over rook placements.",

keywords = "Jordan canonical form, Nilpotent matrices, Q-rook placements, Set partitions",

author = "Martha Yip",

year = "2013",

language = "English",

pages = "1017--1028",

note = "25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 ; Conference date: 24-06-2013 Through 28-06-2013",

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AU - Yip, Martha

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N2 - The set of n by n upper-triangular nilpotent matrices with entries in a finite field Fq has Jordan canonical forms indexed by partitions λ ⊢ n. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number Fλ (q) of matrices of fixed Jordan type as a weighted sum over rook placements.

AB - The set of n by n upper-triangular nilpotent matrices with entries in a finite field Fq has Jordan canonical forms indexed by partitions λ ⊢ n. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number Fλ (q) of matrices of fixed Jordan type as a weighted sum over rook placements.

KW - Jordan canonical form

KW - Nilpotent matrices

KW - Q-rook placements

KW - Set partitions

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UR - http://www.scopus.com/inward/citedby.url?scp=84887437885&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84887437885

SN - 1462-7264

SP - 1017

EP - 1028

JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

T2 - 25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013

Y2 - 24 June 2013 through 28 June 2013

ER -

Q-Rook placements and Jordan forms of upper-triangular nilpotent matrices

Abstract

Keywords

ASJC Scopus subject areas

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