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Showing 1 to 3 of 3 for “"bijective proofs"”.
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Bijective proofs of partition identities and covering systems
… on colored partitions, and they asked for a bijective proof of it. In Chapter 2, we give a bijective proof of a more general partition identity, with the Farkas and Kra partition theorem being a special case. We then derive three further general partition identities and give bijective proofs …
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A q-analogue of spanning trees : nilpotent transformations over finite fields
… Kn. This relationship is based on two similar bijective proofs to calculate the number of spanning trees and nilpotent transformations, respectively. We also discuss more details about this bijection in the cases of complete graphs, complete bipartite graphs, and cycles. It gives some …
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Combinatorics of determinantal identities
… We give linear-algebraic and (new) bijective proofs; the latter also give an extension of the Jacobi ratio theorem. Chapter 4 is dedicated to the celebrated MacMahon master theorem. We present numerous generalizations and applications. In Chapter 5, we study another important result, …