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COMBINATORICS

2004

10 years 6 months ago
2004

We give a combinatorial proof of a q-analogue of the classical formula for the sum of cubes.

COMBINATORICS

2004

10 years 6 months ago
2004

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...

COMBINATORICS

2004

10 years 6 months ago
2004

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

COMBINATORICS

2004

10 years 6 months ago
2004

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...

COMBINATORICS

2004

10 years 6 months ago
2004

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...

COMBINATORICS

2004

10 years 6 months ago
2004

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...

COMBINATORICS

2004

10 years 6 months ago
2004

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...

COMBINATORICS

2004

10 years 6 months ago
2004

COMBINATORICS

2004

10 years 6 months ago
2004

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...

COMBINATORICS

2004

10 years 6 months ago
2004

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...