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COMBINATORICS
2004
96views more  COMBINATORICS 2004»
9 years 3 months ago
A Combinatorial Proof of the Sum of q-Cubes
We give a combinatorial proof of a q-analogue of the classical formula for the sum of cubes.
Kristina C. Garrett, Kristen Hummel
COMBINATORICS
2004
81views more  COMBINATORICS 2004»
9 years 3 months ago
A Card Shuffling Analysis of Deformations of the Plancherel Measure of the Symmetric Group
This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of "cut and then riffle shuffle". This allo...
Jason E. Fulman
COMBINATORICS
2004
94views more  COMBINATORICS 2004»
9 years 3 months ago
A Bijection Between Classes of Fully Packed Loops and Plane Partitions
It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a
P. Di Francesco, Paul Zinn-Justin, Jean-Bernard Zu...
COMBINATORICS
2004
61views more  COMBINATORICS 2004»
9 years 3 months ago
Graphic and Protographic Lists of Integers
A positive list (list of positive integers) is protographic if its merger with all but finitely many positive graphic lists is graphic. Define the family Ps of s-protogaphic lists...
Dmitry Fon-Der-Flaass, Douglas B. West
COMBINATORICS
2004
90views more  COMBINATORICS 2004»
9 years 3 months ago
Strings with Maximally Many Distinct Subsequences and Substrings
A natural problem in extremal combinatorics is to maximize the number of distinct subsequences for any length-n string over a finite alphabet ; this value grows exponentially, but...
Abraham Flaxman, Aram Wettroth Harrow, Gregory B. ...
COMBINATORICS
2004
112views more  COMBINATORICS 2004»
9 years 3 months ago
Airy Phenomena and Analytic Combinatorics of Connected Graphs
Until now, the enumeration of connected graphs has been dealt with by probabilistic methods, by special combinatorial decompositions or by somewhat indirect formal series manipula...
Philippe Flajolet, Bruno Salvy, Gilles Schaeffer
COMBINATORICS
2004
100views more  COMBINATORICS 2004»
9 years 3 months ago
Lattice Structures from Planar Graphs
The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the p...
Stefan Felsner
COMBINATORICS
2004
74views more  COMBINATORICS 2004»
9 years 3 months ago
Voltage Graphs, Group Presentations and Cages
We construct smallest known trivalent graphs for girths 16 and 18. One construction uses voltage graphs, and the other coset enumeration techniques for group presentations. AMS Su...
Geoffrey Exoo
COMBINATORICS
2004
86views more  COMBINATORICS 2004»
9 years 3 months ago
Multiple Pattern Avoidance with respect to Fixed Points and Excedances
We study the distribution of the statistics `number of fixed points' and `number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all th...
Sergi Elizalde
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