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Geometry and combinatorics are two different branches of mathematics. Does there exist any connection between them? In many cases, mathematicians solve some geometric problems by reducing them to a combinatorial language. What are the general techniques to convert a geometrical problem to a combinatorial one? What are the known examples in literature? What will be some good references to learn these techniques?

Thanks in advance.

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  • $\begingroup$ It might be worth having a look at Geombinatorics Quarterly, geombina.uccs.edu $\endgroup$
    – Gerry Myerson
    Commented Sep 8, 2022 at 4:49
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    $\begingroup$ This question is not a duplicate, but a subset of this question, which already has excellent answers: mathoverflow.net/questions/179120/… $\endgroup$
    – domotorp
    Commented Sep 8, 2022 at 7:09
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    $\begingroup$ If you search on "geometric combinatorics" at Amazon, you will find many books on this topic. $\endgroup$
    – Richard Stanley
    Commented Sep 8, 2022 at 14:36

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I would recommend the work of Adiprasito, Huh and Katz:

K. Adiprasito, J. Huh, E. Katz, Hodge Theory for Combinatorial Geometries, Annals of Mathematics 188 (2018), 381–452. [arXiv]. [Journal]

They actually use geometric intuition/techniques to solve problems in combinatorics (rather than using combinatorics to solve geometric problems).

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