An Inequality for Macaulay Functions
Bernardo M. Ábrego and Silvia Fernández-Merchant
Department of Mathematics
California State University, Northridge
18111 Nordhoff Street
Northridge, CA 91330
USA
Bernardo Llano
Departamento de Matemáticas
Universidad Autónoma Metropolitana, Iztapalapa
San Rafael Atlixco 186
Colonia Vicentina, 09340, México, D.F.
México
Abstract:
Given integers

and

, there is a unique way of
writing

as

so
that

. Using this representation,
the
k
Macaulay function of 
is
defined as

We show that if

and

, then

. As a corollary, we obtain a short proof of
Macaulay's theorem. Other previously known results are obtained as
direct consequences.
Full version: pdf,
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(Concerned with sequences
A123578
A123579
A123580
A123731.)
Received December 18 2010;
revised version received July 8 2011.
Published in Journal of Integer Sequences, September 5 2011.
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