Lattice Paths and Determinants

Pamela Ard

Monday, March 22, 2004
1:00 pm, 845 Patterson Office Tower

Abstract:

In "Some Remarks on Ballot-Type Sequences of Positive Integers", Carlitz, Roselle and Scoville consider the problem of determining the number of lattice paths using unit horizontal steps and unit vertical steps from (1,1) to (n+1,f(n)) that do not go above the roof determined by f. The main focus will be on if we have this roof determined by f and assign the number 1 to each cell of the roof, can we assign positive integers to the cells under the roof in such a way that every square subarray comprised of adjacent rows and columns and containing at least one 1 will have determinant 1.