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Lattice Paths, Catalan Numbers and Bijections
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Lattice Paths, Catalan Numbers and Bijections
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Description
Identifier
Thesis
2502
Author
Zering, Jennifer Michelle, 1991
Title
Lattice
Paths
,
Catalan
Numbers
and
Bijections
Publisher
Central Connecticut State University
Date of Publication
2015
Resource Type
Master's Thesis
Abstract
We
prove
that the
number
of
lattice
paths
of
length
2l
+
1
that
begin
at the
origin
and
end
at the
point
(1,0)
; that
do
not
touch
the
negative
xaxis
or the
origin
after
leaving
the
origin
, with
each
step
having
length
one
and
being
parallel
to a
coordinate
axis
,
is
equal
to the
Catalan
number
[equation]
,
using
a
bijective
argument
,
dierent
from the
one
that
can
be
found
in the
literature
. In
Chapter
2
,
we
discuss
the
Catalan
numbers
in
general
,
along
with
some
of their
most
common
combinatorial
interpretations
,
including
rooted
binary
trees
,
binary
strings
, and
lattice
paths
. This
chapter
also
includes
an
algebraic
derivation
of the
formula
for
Catalan
numbers
,
[equation]
. In
Chapter
3
,
we
solve
the
main
problem
using
an
algebraic
method
. This
involves
using
a
generating
function
that
can
be
found
in the
literature
and
extracting
the
relevant
coefcients
. In
Chapter
4
,
we
solve
the
main
problem
using
a
bijection
between
the
sets
of
desired
lattice
paths
and a
set
of
rooted
binary
trees
.
Notes
"
Submitted
in
partial
completion
of the
Requirements
for the
Degree
of
Maste
rof
Arts
in
Mathematics
,
Department
of
Mathematical
Sciences.
";
Advisor
:
Frédéric
Latour.
;
M.A.,Central
Connecticut
State
University,,2015.
;
Includes
bibliographical
references
(leaves
3536)
.
Subject
Lattice paths.
Catalan numbers (Mathematics)
Department
Department of Mathematical Sciences
Advisor
Latour, Frédéric
Type
Text
Digital Format
application/pdf
Software
System requirements: PC and World Wide Web browser.
Language
eng
OCLC number
941157192
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