# 组合数学作业代写Combinatorial mathematics代考

## 组合设计Combinatorial design代写

• 有限几何学Finite geometry
• 序理论Order theory
• 拟阵Matroid
• 极限组合学 Extremal combinatorics

## 组合数学的历史

Basic combinatorial concepts and enumerative results appeared throughout the ancient world. In the 6th century BCE, ancient Indian physician Sushruta asserts in Sushruta Samhita that 63 combinations can be made out of 6 different tastes, taken one at a time, two at a time, etc., thus computing all 26 − 1 possibilities. Greek historian Plutarch discusses an argument between Chrysippus (3rd century BCE) and Hipparchus (2nd century BCE) of a rather delicate enumerative problem, which was later shown to be related to Schröder–Hipparchus numbers.Earlier, in the Ostomachion, Archimedes (3rd century BCE) may have considered the number of configurations of a tiling puzzle, while combinatorial interests possibly were present in lost works by Apollonius.

## 组合数学课后作业代写

We find the cochain, whose coboundary equals the representative of the appropriate power of the Stiefel-Whitney characteristic class by setting
$$K:=\bigoplus_{i=1}^{t} q\left(B_{v_{i}}\right)$$
Indeed, a straightforward coboundary computation yields
\begin{aligned} \partial K &=\bigoplus_{i=1}^{t} \partial q\left(B_{v_{i}}\right)=\bigoplus_{i=1}^{t} q\left(\partial B_{v_{i}}\right) \ &=\bigoplus_{i=1}^{t}\left(q\left(A_{v_{i}-1}\right) \oplus q\left(A_{v_{i}+1}\right)\right)=q\left(A_{r}\right) \oplus q\left(A_{0}\right)=q\left(A_{r}\right) \end{aligned}
hence the sequence of equalities
$$\varpi_{1}^{n-2}\left(X_{r, n}\right)=\left[q\left(A_{r}\right)\right]=[\partial K]=0$$