Sperner theory in partially ordered sets:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Leipzig
Teubner
1985
|
| Edition: | 1. Aufl. |
| Series: | Teubner-Texte zur Mathematik
78 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 213 - 229 |
| Physical Description: | 232 S. graph. Darst. |
Staff View
MARC
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| 100 | 1 | |a Engel, Konrad |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Sperner theory in partially ordered sets |c Konrad Engel ; Hans-Dietrich O. F. Gronau |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Leipzig |b Teubner |c 1985 | |
| 300 | |a 232 S. |b graph. Darst. | ||
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| 490 | 1 | |a Teubner-Texte zur Mathematik |v 78 | |
| 500 | |a Literaturverz. S. 213 - 229 | ||
| 650 | 7 | |a Partiële orde |2 gtt | |
| 650 | 4 | |a Extremal problems (Mathematics) | |
| 650 | 4 | |a Partially ordered sets | |
| 650 | 4 | |a Sperner theory | |
| 650 | 0 | 7 | |a Extremwert |0 (DE-588)4137272-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804116573545299968 |
|---|---|
| adam_text | Contents
1. Introduction 7
1.1. Preliminaries 7
1.2. Notation and terminology 14
1.3. The main examples IB
2. The general Speraer problem 23
2.1. The Sperner problem as an optimization problem .... 23
2.2. Coverings by chains as the dual problem and
Dilworth-type theorems 29
2.3. Normal posets and flow morphisms 34
2.4. Symmetric chain orders 50
2.5. Feck posets and linear algebra methods 56
2.6. An inequality for distributive lattices 72
2.7. Optimal representations of posets 77
2.8. The asymptotic product theorem 86
3. Problems in SCkj.kg,...,kn) 97
3.1. Lexicographic order 98
3.1.1. The Clements-Lindstrbm theorem 98
3.1.2. Estimations of shadows 106
3.1.3. The new-shadow operator 113
3.2. Applications of the Clements-Lindstrttm theorem .... 120
3.2.1. Canonical Sperner families 120
3.2.2. An existence theorem for Sperner families 122
3.2.3. Ideals of minimum weight 124
3.2.4. Maximum adjacencies 125
3.2.5. Minimum ideals with generating families of given
size 127
3.2.6. Minimal number of basic elements 133
3.3. Maximum Sperner families 135
3.3.1. Sperner families 135
3.3.2. Complementfree Sperner families 137
3.3.3. Complementary Sperner families 140
3.3.4. Dynamically Intersecting Sperner families 143
3.3.5. Statically intersecting Sperner families 146
3.4. Erdbs-Ko-Rado type theorems 153
3.4.1. Dynamic intersection 153
3.4.2. Static intersection 154
3.5. Maximum not Sperner families 159
3.5.1. Dynamically intersecting families 159
3.5.2. Statically intersecting families 161
3.5.3. Hamming intersecting families 164
3.5.4. Further results 166
3.6. Further problems 169
4. Profiles of families and extremal problems in the
function poset P? and the cubical poset Cn 172
4.1. Profiles of families and their convex closure 173
4.2. The intersection condition in the function poset ?£ 177
4.3. Profile polyhedra for the cubical poset Cn 183
5. The eigenvalue method and intersection problems in
the linear lattice Ln(q) 186
5.1. An upper bound for the independence number of a
regular graph 186
5.2. Intersection theorems for the linear lattice Ln(q) 189
6. Applications 196
6.1. Number of monotone Boolean functions 196
6.2. Boolean functions of maximum length 198
6.3. Recognition of order-preserving functions 200
6.4. Problems in relational data base 203
6.5. The Littlewood-Offord problem 204
6.6. Hilbert s base theorem 205
6.7. The Erdos-Moser problem 206
6.8. An inequality for Bernstein polynomials 208
6.9. A continuous Sperner type theorem 209
6.10. Three further applications 211
References „. 213
Subject index 230
|
| any_adam_object | 1 |
| author | Engel, Konrad Gronau, Hans-Dietrich 1951- |
| author_GND | (DE-588)138612498 |
| author_facet | Engel, Konrad Gronau, Hans-Dietrich 1951- |
| author_role | aut aut |
| author_sort | Engel, Konrad |
| author_variant | k e ke h d g hdg |
| building | Verbundindex |
| bvnumber | BV002120242 |
| callnumber-first | Q - Science |
| callnumber-label | QA171 |
| callnumber-raw | QA171.485 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 150 SK 890 |
| classification_tum | MAT 065f MAT 050f |
| ctrlnum | (OCoLC)13727493 (DE-599)BVBBV002120242 |
| dewey-full | 511.3/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/2 |
| dewey-search | 511.3/2 |
| dewey-sort | 3511.3 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Book |
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| indexdate | 2024-07-09T15:40:39Z |
| institution | BVB |
| language | English |
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| physical | 232 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Engel, Konrad Verfasser aut Sperner theory in partially ordered sets Konrad Engel ; Hans-Dietrich O. F. Gronau 1. Aufl. Leipzig Teubner 1985 232 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 78 Literaturverz. S. 213 - 229 Partiële orde gtt Extremal problems (Mathematics) Partially ordered sets Sperner theory Extremwert (DE-588)4137272-4 gnd rswk-swf Sperner-Satz (DE-588)4128925-0 gnd rswk-swf Extremalproblem (DE-588)4439315-5 gnd rswk-swf Halbgeordnete Menge (DE-588)4128951-1 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Sperner-Satz (DE-588)4128925-0 s Halbgeordnete Menge (DE-588)4128951-1 s DE-604 Extremalproblem (DE-588)4439315-5 s 2\p DE-604 Extremwert (DE-588)4137272-4 s 3\p DE-604 Gronau, Hans-Dietrich 1951- Verfasser (DE-588)138612498 aut Teubner-Texte zur Mathematik 78 (DE-604)BV000012607 78 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001390193&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Engel, Konrad Gronau, Hans-Dietrich 1951- Sperner theory in partially ordered sets Teubner-Texte zur Mathematik Partiële orde gtt Extremal problems (Mathematics) Partially ordered sets Sperner theory Extremwert (DE-588)4137272-4 gnd Sperner-Satz (DE-588)4128925-0 gnd Extremalproblem (DE-588)4439315-5 gnd Halbgeordnete Menge (DE-588)4128951-1 gnd |
| subject_GND | (DE-588)4137272-4 (DE-588)4128925-0 (DE-588)4439315-5 (DE-588)4128951-1 (DE-588)4113937-9 |
| title | Sperner theory in partially ordered sets |
| title_auth | Sperner theory in partially ordered sets |
| title_exact_search | Sperner theory in partially ordered sets |
| title_full | Sperner theory in partially ordered sets Konrad Engel ; Hans-Dietrich O. F. Gronau |
| title_fullStr | Sperner theory in partially ordered sets Konrad Engel ; Hans-Dietrich O. F. Gronau |
| title_full_unstemmed | Sperner theory in partially ordered sets Konrad Engel ; Hans-Dietrich O. F. Gronau |
| title_short | Sperner theory in partially ordered sets |
| title_sort | sperner theory in partially ordered sets |
| topic | Partiële orde gtt Extremal problems (Mathematics) Partially ordered sets Sperner theory Extremwert (DE-588)4137272-4 gnd Sperner-Satz (DE-588)4128925-0 gnd Extremalproblem (DE-588)4439315-5 gnd Halbgeordnete Menge (DE-588)4128951-1 gnd |
| topic_facet | Partiële orde Extremal problems (Mathematics) Partially ordered sets Sperner theory Extremwert Sperner-Satz Extremalproblem Halbgeordnete Menge Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001390193&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
| work_keys_str_mv | AT engelkonrad spernertheoryinpartiallyorderedsets AT gronauhansdietrich spernertheoryinpartiallyorderedsets |