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BSL
2000
13 years 9 months ago
2000
We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially or...
COMBINATORICS
2000
13 years 9 months ago
2000
Let d(n) count the lattice paths from (0, 0) to (n, n) using the steps (0,1), (1,0), and (1,1). Let e(n) count the lattice paths from (0, 0) to (n, n) with permitted steps from th...
COMBINATORICS
2000
13 years 9 months ago
2000
The question of whether the characteristic polynomial of a simple graph is uniquely determined by the characteristic polynomials of its vertex-deleted subgraphs is one of the many...
COMBINATORICS
2000
13 years 9 months ago
2000
A counterexample is presented to Gy. Elekes's conjecture concerning the existence of long 2-colored paths in properly colored graphs. A modified version of the conjecture is ...
COMBINATORICS
2000
13 years 9 months ago
2000
The lattice of the set partitions of [n] ordered by refinement is studied. Suppose r partitions p1, . . . , pr are chosen independently and uniformly at random. The probability tha...