For questions about the study of finite or countable discrete structures, specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

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2
votes
1answer
221 views
+100

Positivity of the alternating sum associated to at most five subspaces

Let $V_1 , V_2 , \dots , V_n $ be proper subspaces of $ \mathbb{C}^m$ and let $$\alpha = \sum_{r=1}^n (-1)^{r+1} \sum_{ \ i_1 < i_2 < \cdots < i_r } dim(V_{i_1} \cap \cdots \cap V_{i_r})$$ ...
3
votes
1answer
47 views
+50

Find the maximum number of people who participated in exactly three games?

Gauri Apartment housing society organised annual games, consisting of three games: snooker, badminton and tennis. In all, $510$ people were members in the apartments' society and they were ...
0
votes
1answer
27 views
+50

Finding the data regarding the four racket games.

In a vijantkhand sports stadium, athletes choose from $4$ different racket games (apart from athletes which is compulsory for all) These are tennis, table tennis, squash and badminton. It is ...
0
votes
1answer
92 views
+50

all but one sub-strings within a cyclic string

over $GF(q)$ where $q\in\mathbb{N}$, we build a string of size $q^n-1$. now, how can I show that it is always possible to construct that string so it contains all sub-strings of size $n$ exactly once, ...