What is combinatorics? - Mathematics Stack Exchange
Personally, I see "combinatorics" as the "art of counting", which implies that the underlying objects are at least countable (= discrete), but better finite. I find it natural that "graph theory" is filed under …
What is a combinatorial proof exactly? - Mathematics Stack Exchange
Jan 11, 2016 · The essence of a combinatorial proof is to provide a bijection between the elements of a known set and the elements of the set under consideration. A nice characterization is given by R.P. …
What is the definition of a combinatorial game?
Mar 16, 2026 · I am trying to see if combinatorial game theory is worth investing time in. The most natural question is then what is the basic object of study in that field, i.e., what is the definition of a …
Proof of the hockey stick/Zhu Shijie identity $\sum\limits_ {t=0}^n ...
Let me add one purely-combinatorial proof. : the justification for doing so is that I think we can tell this in a "committee-forming" way that is used for other identities (e.g. Pascal's rule), without needing to …
Newest 'combinatorics' Questions - Mathematics Stack Exchange
2 days ago · For questions about the study of finite or countable discrete structures, especially how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes …
Permutations vs. Combinatorial vs. Factorials vs. Exponents
Nov 25, 2018 · I'm currently working on a probability course, and I am constantly having trouble figuring out when to use permutations vs. combinations vs. factorials vs. exponents in order to calculate …
Proof of Theorem on Punctured Combinatorial Nullstellensatz
Feb 24, 2025 · I am reading the proof of this corollary from "Punctured Combinatorial Nullstellensatz" by Ball and Serra, and there is a crucial step in the proof that I am struggling to …
combinatorial proofs - Combinatoric identity - Mathematics Stack …
Mar 18, 2024 · 1 I'm trying to get a combinatorial proof of the following identity by making up some story. $$\sum_ {k=1}^n {k \choose j}k = {n+1 \choose j+1}n - {n+1 \choose j+2}$$ I can do it, by simplifying …
Book on combinatorial identities - Mathematics Stack Exchange
Oct 9, 2014 · Do you know any good book that deals extensively with identities obtained using combinatorial and/or probabilistic arguments (e.g., by solving the same combinatorial or probability …
Why algebraic topology is also called combinatorial topology?
Combinatorial topology is the older name for algebraic topology when all topological problems were expressed, set up and solved in Euclidean space of dimensions 1,2 and 3.