A Combinatorial Proof of Louck's Conjecture
Séminaire lotharingien de combinatoire, Tome 20 (1988)
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The conjecture in question deals with a function of several variables indexed by a sequence of integers that is to be expressed as a sum of convolution products of functions of the same kind. The combinatorial proof given here is based on a careful study of connectedness of finite structures whose generating polynomials are precisely the functions in question.
@article{SLC_1988_20_a6,
author = {Volker Strehl},
title = {A {Combinatorial} {Proof} of {Louck's} {Conjecture}},
journal = {S\'eminaire lotharingien de combinatoire},
year = {1988},
volume = {20},
url = {http://geodesic.mathdoc.fr/item/SLC_1988_20_a6/}
}
Volker Strehl. A Combinatorial Proof of Louck's Conjecture. Séminaire lotharingien de combinatoire, Tome 20 (1988). http://geodesic.mathdoc.fr/item/SLC_1988_20_a6/