Partial bijection

Lecture Discrete mathematics: Chapter 2.2 provide students with content about: definition of a function; domain, codomain; image, preimage; injection, surjection, bijection; inverse function; function composition; graphing functions; floor, ceiling, factorial; partial functions (optional);... Please refer to the detailed lecture content!

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Let In be the symmetric inverse semigroup, and let PODIn and POIn be its subsemigroups of monotone partial bijections and of isotone partial bijections on Xn = {1, . . . , n} under its natural order, respectively.

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