The number of requests in the Garsia-Milne involution principle follows a hypergeometric distribution under a random assignment model, with a geometric limit.
A bijective proof of the ASM theorem, Part I: the operator formula
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abstract
Alternating sign matrices are known to be equinumerous with descending plane partitions, totally symmetric self-complementary plane partitions and alternating sign triangles, but no bijective proof for any of these equivalences has been found so far. In this paper we provide the first bijective proof of the operator formula for monotone triangles, which has been the main tool for several non-combinatorial proofs of such equivalences. In this proof, signed sets and sijections (signed bijections) play a fundamental role.
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Experimenting with the Garsia-Milne Involution Principle
The number of requests in the Garsia-Milne involution principle follows a hypergeometric distribution under a random assignment model, with a geometric limit.