Results 211 to 220 of about 8,473 (239)
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Constructing sequential bijections
1997We state a simple condition on a rational subset X of a free monoid B* for the existence of a sequential function that is a one-to-one mapping of some free monoid A* onto X. As a by-product we obtain new sequential bijections of a free monoid onto another.
Christophe Prieur 0002 +2 more
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A Bijective Proof of a Theorem of Knuth
Combinatorics, Probability and Computing, 2010The line graph G of a directed graph G has a vertex for every edge of G and an edge for every path of length 2 in G. In 1967, Knuth used the Matrix Tree Theorem to prove a formula for the number of spanning trees of G, and he asked for a bijective proof [6]. In this paper, we give a bijective proof of Knuth's formula. As a result of this proof, we find
Hoda Bidkhori, Shaunak Kishore
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An Extension of Franklin’s Bijection
2001The author gives a purely combinatorial proof of the identity \[ \prod_{n>m}(1-q^n) = \sum_{n=1}^{\infty} (-1)^n \left[ {n+m \atop m} \right] q^{nm+n(3n+1)/2}(1-q^{2n+m+1}), \] which generalizes Franklin's proof for the case \(m=0\).
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Reversible and Bijectively Related Posets
Order, 2009A poset is said to be reversible if every of its order-preserving self-bijections is an automorphism. Three classes of reversible posets are described: 1) Every poset \(P\) of height 2 that has finitely many connected components and contains finitely many crowns is reversible. 2) Let \(P\) be a well-founded poset such that every level \(P_{\alpha}\), \(
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The q-Variations of Sylvester’s Bijection Between Odd and Strict Partitions
Ramanujan Journal, 2005Jiang Zeng
exaly
On a functional equation involving iterates of a bijection on the unit interval
Nonlinear Analysis: Theory, Methods & Applications, 1983Arunava Mukherjea
exaly