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Yes. The following Atlas Search operators support partial string matching queries:
Yes. You can use the wildcard and regex operators with a custom analyzer to perform a case-insensitive search. You can define a custom analyzer with the following tokenizer and token filter to perform a wildcard case-insensitive search:
No, you can't use the shard key to run Atlas Search queries on a specific shard or a subset of shards. In a sharded cluster environment, Atlas Search queries are scatter-gather queries that run on all the shards.