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- W4300375698 abstract "In this paper, we study a family of lattice walks which are related to the Hadamard conjecture. There is a bijection between paths of these walks which originate and terminate at the origin and equivalence classes of partial Hadamard matrices. Therefore, the existence of partial Hadamard matrices can be proved by showing that there is positive probability of a random walk returning to the origin after a specified number of steps. Moreover, the number of these designs can be approximated by estimating the return probabilities. We use the inversion formula for the Fourier transform of the random walk to provide such estimates. We also include here an upper bound, derived by elementary methods, on the number of partial Hadamard." @default.
- W4300375698 created "2022-10-03" @default.
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- W4300375698 date "2010-03-21" @default.
- W4300375698 modified "2023-09-27" @default.
- W4300375698 title "A Fourier-analytic Approach to Counting Partial Hadamard Matrices" @default.
- W4300375698 doi "https://doi.org/10.48550/arxiv.1003.4003" @default.
- W4300375698 hasPublicationYear "2010" @default.
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