Results 171 to 180 of about 116,873 (193)
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2013
On considere le produit infini (1 + x)(1 + x2)(1 + x3)(1 + x4) ⋯ que l’on developpe selon la methode habituelle sous la forme d’une serie \( \sum {_{n \geqslant 0} a_n x^n } \) en regroupant les termes correspondant a la meme puissance de x.
Martin Aigner, Günter M. Ziegler
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On considere le produit infini (1 + x)(1 + x2)(1 + x3)(1 + x4) ⋯ que l’on developpe selon la methode habituelle sous la forme d’une serie \( \sum {_{n \geqslant 0} a_n x^n } \) en regroupant les termes correspondant a la meme puissance de x.
Martin Aigner, Günter M. Ziegler
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The American Mathematical Monthly, 2019
When is a function from an abelian group to itself expressible as a difference of two bijections? Answering this question for finite cyclic groups solves a problem about juggling.
Daniel H. Ullman, Daniel J. Velleman
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When is a function from an abelian group to itself expressible as a difference of two bijections? Answering this question for finite cyclic groups solves a problem about juggling.
Daniel H. Ullman, Daniel J. Velleman
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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 +2 more
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2009
Nous montrons que toute bijection de Pn(K), pour K un corps fini de caractéristique impaire, est induite par une transformation birationnelle sans point d'indétermination ...
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Nous montrons que toute bijection de Pn(K), pour K un corps fini de caractéristique impaire, est induite par une transformation birationnelle sans point d'indétermination ...
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2004
Consider the infinite product (1+x)(1+x 2)(1+x 3)(1+x 4) · · · and expand it in the usual way into a series \( \sum_{n \geq 0} \) a n x n by grouping together those products that yield the same power x n . By inspection we find for the first terms $$ \label{1} \prod_{k \geq 1} (1+x^{k}) = 1 + x + x^{2} + 2x^{3} + 2x^{4} + 3x^{5} + 4x^{6} + 5x^{7} +
Martin Aigner, Günter M. Ziegler
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Consider the infinite product (1+x)(1+x 2)(1+x 3)(1+x 4) · · · and expand it in the usual way into a series \( \sum_{n \geq 0} \) a n x n by grouping together those products that yield the same power x n . By inspection we find for the first terms $$ \label{1} \prod_{k \geq 1} (1+x^{k}) = 1 + x + x^{2} + 2x^{3} + 2x^{4} + 3x^{5} + 4x^{6} + 5x^{7} +
Martin Aigner, Günter M. Ziegler
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20th Annual Symposium on Foundations of Computer Science (sfcs 1979), 1979
In this paper we study bijective a-transducers. We derive necessary and sufficient conditions on pairs of regular sets (R,S) such that a bijective a-transducer, mapping R cnto S exists. The results obtained allow the systematic construction of an a-transducer, mapping a set R onto a set S bijectively for surprisingly "different" regular sets R and S.
H. A. Maurer, H. Nivat
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In this paper we study bijective a-transducers. We derive necessary and sufficient conditions on pairs of regular sets (R,S) such that a bijective a-transducer, mapping R cnto S exists. The results obtained allow the systematic construction of an a-transducer, mapping a set R onto a set S bijectively for surprisingly "different" regular sets R and S.
H. A. Maurer, H. Nivat
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2012
Two problems, connected with analysing empirical data are considered. First is a problem of minimizing the number of crossings in a bipartite graph. Second is a pattern matching problem for permutations. In both cases the original problem is transformed into a similar problem for an appropriate mathematical structure, which can be considered as an ...
Vohandu Leo, Peder Ahti, Tombak Mati
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Two problems, connected with analysing empirical data are considered. First is a problem of minimizing the number of crossings in a bipartite graph. Second is a pattern matching problem for permutations. In both cases the original problem is transformed into a similar problem for an appropriate mathematical structure, which can be considered as an ...
Vohandu Leo, Peder Ahti, Tombak Mati
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Bijective Class of Replicator Equations
Mathematical NoteszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mukhamedov, F. M. +2 more
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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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