Orbits of rational n-sets of projective spaces under the action of the linear group

Ricard Martí; Enric Nart

doi:10.1016/j.jcta.2007.08.002

Orbits of rational n-sets of projective spaces under the action of the linear group

Ricard Martí, Enric Nart

Departament de Matemàtiques

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Let k = Fq be a finite field. We enumerate k-rational n-sets of (unordered) points in a projective space PN over k, and we compute the generating function for the numbers of PGLN + 1 (k)-orbits of these n-sets. For N = 1, 2 we obtain a formula for these numbers of orbits as a polynomial in q with integer coefficients. © 2007 Elsevier Inc. All rights reserved.

Idioma original	Anglès
Pàgines (de-a)	547-568
Revista	Journal of Combinatorial Theory - Series A
Volum	115
DOIs	https://doi.org/10.1016/j.jcta.2007.08.002
Estat de la publicació	Publicada - 1 de maig 2008

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10.1016/j.jcta.2007.08.002

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title = "Orbits of rational n-sets of projective spaces under the action of the linear group",

abstract = "Let k = Fq be a finite field. We enumerate k-rational n-sets of (unordered) points in a projective space PN over k, and we compute the generating function for the numbers of PGLN + 1 (k)-orbits of these n-sets. For N = 1, 2 we obtain a formula for these numbers of orbits as a polynomial in q with integer coefficients. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

keywords = "Finite field, Finite poset, Generating function, Projective linear group, Projective space, Rational n-set, Zeta function",

author = "Ricard Mart{\'i} and Enric Nart",

year = "2008",

month = may,

day = "1",

doi = "10.1016/j.jcta.2007.08.002",

language = "English",

volume = "115",

pages = "547--568",

journal = "Journal of Combinatorial Theory - Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Orbits of rational n-sets of projective spaces under the action of the linear group

AU - Martí, Ricard

AU - Nart, Enric

PY - 2008/5/1

Y1 - 2008/5/1

N2 - Let k = Fq be a finite field. We enumerate k-rational n-sets of (unordered) points in a projective space PN over k, and we compute the generating function for the numbers of PGLN + 1 (k)-orbits of these n-sets. For N = 1, 2 we obtain a formula for these numbers of orbits as a polynomial in q with integer coefficients. © 2007 Elsevier Inc. All rights reserved.

AB - Let k = Fq be a finite field. We enumerate k-rational n-sets of (unordered) points in a projective space PN over k, and we compute the generating function for the numbers of PGLN + 1 (k)-orbits of these n-sets. For N = 1, 2 we obtain a formula for these numbers of orbits as a polynomial in q with integer coefficients. © 2007 Elsevier Inc. All rights reserved.

KW - Finite field

KW - Finite poset

KW - Generating function

KW - Projective linear group

KW - Projective space

KW - Rational n-set

KW - Zeta function

U2 - 10.1016/j.jcta.2007.08.002

DO - 10.1016/j.jcta.2007.08.002

M3 - Article

SN - 0097-3165

VL - 115

SP - 547

EP - 568

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

ER -

Orbits of rational n-sets of projective spaces under the action of the linear group

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