On Elements of Finite Semigroups of Order-Preserving and Decreasing Transformations
For n ∈ N , let C n be the semigroup of all order-preserving and decreasing transformations on X n = { 1 , … , n } , under its natural order, and let N ( C n ) be the set of all nilpotent elements of C n and let Fix ( α ) = { x ∈ X n : x α = x } for any transformation α . An element a of a finite se...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2020-09, Vol.43 (5), p.3863-3870 |
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| creator | Yağcı, Melek Korkmaz, Emrah |
| description | For
n
∈
N
, let
C
n
be the semigroup of all order-preserving and decreasing transformations on
X
n
=
{
1
,
…
,
n
}
, under its natural order, and let
N
(
C
n
)
be the set of all nilpotent elements of
C
n
and let
Fix
(
α
)
=
{
x
∈
X
n
:
x
α
=
x
}
for any transformation
α
. An element
a
of a finite semigroup is called
m
-potent (
m
-nilpotent) element if
a
m
+
1
=
a
m
(
a
m
=
0
) and
a
,
a
2
,
…
,
a
m
are distinct. In this paper, we obtain a formulae for the number of
m
-nilpotent elements and so the number of
m
-potent elements in
N
(
C
n
)
for
1
≤
m
≤
n
-
1
. Moreover, for any subset
Y
of
X
n
, we obtain a formulae for the number of
m
-potent elements of
C
n
,
Y
=
{
α
∈
C
n
:
Fix
(
α
)
=
Y
}
. |
| doi_str_mv | 10.1007/s40840-020-00899-7 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2450337281</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2450337281</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-f2b8f6c49734d0fe1f337647afc62333f70dd5920464670cf77cd07501feb46f3</originalsourceid><addsrcrecordid>eNp9kE9LAzEQxYMoWLRfwNOC5-jkzya7R6mtCoUKreew3Z2ULd1snWwFv71pK3hzYBgyvPcm_Bi7E_AgAOxj1FBo4CBTQ1GW3F6wkRQFcC3BXLIRCGm4sZBfs3GMW0iVG2mkGLHlImTTHXYYhpj1Ppu1oR0wW2LXbqg_7E_LBTVI_J0wIn21YZNVocmesSas4vG5oipE31NXDW0f4i278tUu4vh33rCP2XQ1eeXzxcvb5GnOa2lh4F6uC29qXVqlG_AovFLWaFv52killLfQNHkpQRudPl97a-sGbA7C41obr27Y_Tl3T_3nAePgtv2BQjrppM4hpclCJJU8q2rqYyT0bk9tV9G3E-CO_NyZn0v83Imfs8mkzqaYxGGD9Bf9j-sHIm9yQQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2450337281</pqid></control><display><type>article</type><title>On Elements of Finite Semigroups of Order-Preserving and Decreasing Transformations</title><source>SpringerLink Journals - AutoHoldings</source><creator>Yağcı, Melek ; Korkmaz, Emrah</creator><creatorcontrib>Yağcı, Melek ; Korkmaz, Emrah</creatorcontrib><description>For
n
∈
N
, let
C
n
be the semigroup of all order-preserving and decreasing transformations on
X
n
=
{
1
,
…
,
n
}
, under its natural order, and let
N
(
C
n
)
be the set of all nilpotent elements of
C
n
and let
Fix
(
α
)
=
{
x
∈
X
n
:
x
α
=
x
}
for any transformation
α
. An element
a
of a finite semigroup is called
m
-potent (
m
-nilpotent) element if
a
m
+
1
=
a
m
(
a
m
=
0
) and
a
,
a
2
,
…
,
a
m
are distinct. In this paper, we obtain a formulae for the number of
m
-nilpotent elements and so the number of
m
-potent elements in
N
(
C
n
)
for
1
≤
m
≤
n
-
1
. Moreover, for any subset
Y
of
X
n
, we obtain a formulae for the number of
m
-potent elements of
C
n
,
Y
=
{
α
∈
C
n
:
Fix
(
α
)
=
Y
}
.</description><identifier>ISSN: 0126-6705</identifier><identifier>EISSN: 2180-4206</identifier><identifier>DOI: 10.1007/s40840-020-00899-7</identifier><language>eng</language><publisher>Singapore: Springer Singapore</publisher><subject>Applications of Mathematics ; Mathematics ; Mathematics and Statistics ; Transformations ; Yttrium</subject><ispartof>Bulletin of the Malaysian Mathematical Sciences Society, 2020-09, Vol.43 (5), p.3863-3870</ispartof><rights>Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2020</rights><rights>Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-f2b8f6c49734d0fe1f337647afc62333f70dd5920464670cf77cd07501feb46f3</cites><orcidid>0000-0002-0457-156X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40840-020-00899-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40840-020-00899-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Yağcı, Melek</creatorcontrib><creatorcontrib>Korkmaz, Emrah</creatorcontrib><title>On Elements of Finite Semigroups of Order-Preserving and Decreasing Transformations</title><title>Bulletin of the Malaysian Mathematical Sciences Society</title><addtitle>Bull. Malays. Math. Sci. Soc</addtitle><description>For
n
∈
N
, let
C
n
be the semigroup of all order-preserving and decreasing transformations on
X
n
=
{
1
,
…
,
n
}
, under its natural order, and let
N
(
C
n
)
be the set of all nilpotent elements of
C
n
and let
Fix
(
α
)
=
{
x
∈
X
n
:
x
α
=
x
}
for any transformation
α
. An element
a
of a finite semigroup is called
m
-potent (
m
-nilpotent) element if
a
m
+
1
=
a
m
(
a
m
=
0
) and
a
,
a
2
,
…
,
a
m
are distinct. In this paper, we obtain a formulae for the number of
m
-nilpotent elements and so the number of
m
-potent elements in
N
(
C
n
)
for
1
≤
m
≤
n
-
1
. Moreover, for any subset
Y
of
X
n
, we obtain a formulae for the number of
m
-potent elements of
C
n
,
Y
=
{
α
∈
C
n
:
Fix
(
α
)
=
Y
}
.</description><subject>Applications of Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Transformations</subject><subject>Yttrium</subject><issn>0126-6705</issn><issn>2180-4206</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEQxYMoWLRfwNOC5-jkzya7R6mtCoUKreew3Z2ULd1snWwFv71pK3hzYBgyvPcm_Bi7E_AgAOxj1FBo4CBTQ1GW3F6wkRQFcC3BXLIRCGm4sZBfs3GMW0iVG2mkGLHlImTTHXYYhpj1Ppu1oR0wW2LXbqg_7E_LBTVI_J0wIn21YZNVocmesSas4vG5oipE31NXDW0f4i278tUu4vh33rCP2XQ1eeXzxcvb5GnOa2lh4F6uC29qXVqlG_AovFLWaFv52killLfQNHkpQRudPl97a-sGbA7C41obr27Y_Tl3T_3nAePgtv2BQjrppM4hpclCJJU8q2rqYyT0bk9tV9G3E-CO_NyZn0v83Imfs8mkzqaYxGGD9Bf9j-sHIm9yQQ</recordid><startdate>20200901</startdate><enddate>20200901</enddate><creator>Yağcı, Melek</creator><creator>Korkmaz, Emrah</creator><general>Springer Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-0457-156X</orcidid></search><sort><creationdate>20200901</creationdate><title>On Elements of Finite Semigroups of Order-Preserving and Decreasing Transformations</title><author>Yağcı, Melek ; Korkmaz, Emrah</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-f2b8f6c49734d0fe1f337647afc62333f70dd5920464670cf77cd07501feb46f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Applications of Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Transformations</topic><topic>Yttrium</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yağcı, Melek</creatorcontrib><creatorcontrib>Korkmaz, Emrah</creatorcontrib><collection>CrossRef</collection><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yağcı, Melek</au><au>Korkmaz, Emrah</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Elements of Finite Semigroups of Order-Preserving and Decreasing Transformations</atitle><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle><stitle>Bull. Malays. Math. Sci. Soc</stitle><date>2020-09-01</date><risdate>2020</risdate><volume>43</volume><issue>5</issue><spage>3863</spage><epage>3870</epage><pages>3863-3870</pages><issn>0126-6705</issn><eissn>2180-4206</eissn><abstract>For
n
∈
N
, let
C
n
be the semigroup of all order-preserving and decreasing transformations on
X
n
=
{
1
,
…
,
n
}
, under its natural order, and let
N
(
C
n
)
be the set of all nilpotent elements of
C
n
and let
Fix
(
α
)
=
{
x
∈
X
n
:
x
α
=
x
}
for any transformation
α
. An element
a
of a finite semigroup is called
m
-potent (
m
-nilpotent) element if
a
m
+
1
=
a
m
(
a
m
=
0
) and
a
,
a
2
,
…
,
a
m
are distinct. In this paper, we obtain a formulae for the number of
m
-nilpotent elements and so the number of
m
-potent elements in
N
(
C
n
)
for
1
≤
m
≤
n
-
1
. Moreover, for any subset
Y
of
X
n
, we obtain a formulae for the number of
m
-potent elements of
C
n
,
Y
=
{
α
∈
C
n
:
Fix
(
α
)
=
Y
}
.</abstract><cop>Singapore</cop><pub>Springer Singapore</pub><doi>10.1007/s40840-020-00899-7</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0002-0457-156X</orcidid></addata></record> |
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| ispartof | Bulletin of the Malaysian Mathematical Sciences Society, 2020-09, Vol.43 (5), p.3863-3870 |
| issn | 0126-6705 2180-4206 |
| language | eng |
| recordid | cdi_proquest_journals_2450337281 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Applications of Mathematics Mathematics Mathematics and Statistics Transformations Yttrium |
| title | On Elements of Finite Semigroups of Order-Preserving and Decreasing Transformations |
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