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  • 1
    Book
    Book
    Enumerative combinatorics (1986)
    Inc., Belmont, CA :Wadsworth,
    Details
    Title: Enumerative combinatorics
    Author: Stanley, Richard P.
    Publisher: Inc., Belmont, CA :Wadsworth,
    Year of publication: 1986
    Pages: 306 S.
    Series Statement: ¬The¬ Wadsworth & Brooks/Cole Mathematics Series
    Type of Medium: Book
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    Zuse Institute Berlin get availability status
  • 2
    Book
    Book
    Combinatorics and commutative algebra; 41 (1996)
    Basel u.a. :Birkhäuser,
    Details
    Title: Combinatorics and commutative algebra; 41
    Author: Stanley, Richard P.
    Publisher: Basel u.a. :Birkhäuser,
    Year of publication: 1996
    Pages: 164 S.
    Series Statement: Progress in mathematics 41
    Type of Medium: Book
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  • 3
    Electronic Resource
    Electronic Resource
    Two poset polytopes (1986)
    Springer
    Discrete & computational geometry 1 (1986), S. 9-23 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Two convex polytopes, called theorder polytope ϑ(P) andchain polytope ℒ(P), are associated with a finite posetP. There is a close interplay between the combinatorial structure ofP and the geometric structure of ϑ(P). For instance, the order polynomial Ω(P, m) ofP and Ehrhart polynomiali(ϑ(P),m) of ϑ(P) are related by Ω(P, m+1)=i(ϑ(P),m). A “transfer map” then allows us to transfer properties of ϑ(P) to ℒ(P). In particular, we transfer known inequalities involving linear extensions ofP to some new inequalities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187680
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Spanning trees and a conjecture of Kontsevich (1998)
    Springer
    Annals of combinatorics 2 (1998), S. 351-363 
    Details
    ISSN: 0219-3094
    Keywords: 05E99 ; spanning tree ; Matrix-Tree Theorem ; orthogonal geometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Kontsevich conjectured that the number of zeros over the fieldF q of a certain polynomialQ G associated with the spanning trees of a graphG is a polynomial function ofq. We show the connection between this conjecture, the Matrix-Tree Theorem, and orthogonal geometry. We verify the conjecture in certain cases, such as the complete graph, and discuss some modifications and extensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01608530
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Log-Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 576 (1989), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1989.tb16434.x
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  • 6
    Electronic Resource
    Electronic Resource
    Plane Partitions: Past, Present, and Future (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 555 (1989), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1989.tb22478.x
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  • 7
    Electronic Resource
    Electronic Resource
    THE NUMBER OF FACES OF SIMPLICIAL POLYTOPES AND SPHERES (1985)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 440 (1985), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1985.tb14556.x
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  • 8
    Electronic Resource
    Electronic Resource
    Linear diophantine equations and local cohomology (1982)
    Springer
    Inventiones mathematicae 68 (1982), S. 175-193 
    Details
    ISSN: 1432-1297
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01394054
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    On the number of faces of centrally-symmetric simplicial polytopes (1987)
    Springer
    Graphs and combinatorics 3 (1987), S. 55-66 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract I. Bárány and L. Lovász [Acta Math. Acad. Sci. Hung.40, 323–329 (1982)] showed that ad-dimensional centrally-symmetric simplicial polytopeP has at least 2 d facets, and conjectured a lower bound for the numberf i ofi-dimensional faces ofP in terms ofd and the numberf 0 =2n of vertices. Define integers $$h_0 ,...,h_d {\mathbf{ }}by{\mathbf{ }}\sum\limits_{i = 0}^d {f_{i - 1} } (x - 1)^{d - i} = \sum\limits_{i = 0}^d {h_i x^{d - i} } $$ A. Björner conjectured (unpublished) that $$h_i \geqslant \left( {\begin{array}{*{20}c} d \\ i \\ \end{array} } \right)$$ (which generalizes the result of Bárány-Lovász sincef d−1 =∑ h i ), and more strongly that $$h_i - h_{i - 1} \geqslant \left( {\begin{array}{*{20}c} d \\ i \\ \end{array} } \right) - \left( {\begin{array}{*{20}c} d \\ {i - 1} \\ \end{array} } \right),1 \leqslant i \leqslant \left\lfloor {{d \mathord{\left/ {\vphantom {d 2}} \right. \kern-\nulldelimiterspace} 2}} \right\rfloor $$ , which is easily seen to imply the conjecture of Bárány-Lovász. In this paper the conjectures of Björner are proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01788529
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  • 10
    Electronic Resource
    Electronic Resource
    Quotients of peck posets (1984)
    Springer
    Order 1 (1984), S. 29-34 
    Details
    ISSN: 1572-9273
    Keywords: Primary 06A10 ; secondary 05C60 ; 20B25 ; Poset ; Peck poset ; Sperner property ; automorphism group ; quotient poset ; edge-reconstruction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An elementary, self-contained proof of a result of Pouzet and Rosenberg and of Harper is given. This result states that the quotient of certain posets (called unitary Peck) by a finite group of automorphisms retains some nice properties, including the Sperner property. Examples of unitary Peck posets are given, and the techniques developed here are used to prove a result of Lovász on the edge-reconstruction conjecture.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396271
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    Paper (German National Licenses)
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