The topological \(K^{*}\) ring is one of the important tools used for understanding the topology of a manifold. We settle a problem of computing the \(K^{*}\) ring of complex projective Stiefel manifold using combinatorics. We calculate \(K^{*}\) ring of the right generalized projective Stiefel manifold, denoted by \(P_{\ell }W_{n,k}\) , which gives us description of complex \(K^{*}\) ring of complex projective Stiefel manifold \(PW_{n,k}\), which is a particular case of \(P_{\ell }W_{n,k}\).

中文翻译：

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复杂射影Stiefel流形的复杂$$ K ^ {** $$ K *环

拓扑\（K ^ {*} \）环是用于了解流形拓扑的重要工具之一。我们解决了一个使用组合算术计算复射影Stiefel流形的\（K ^ {*} \）环的问题。我们计算右广义广义Stiefel流形的\（K ^ {*} \）环，记为\（P _ {\ ell} W_ {n，k} \），这为我们提供了复数\（K ^ {* } \）复射影Stiefel流形\（PW_ {n，k} \）的环，这是\（P _ {\ ell} W_ {n，k} \）的特例。