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  • 1
    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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  • 2
    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)
    Fulltext
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