An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolu...An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.展开更多
In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spacesℝn^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spacesℝn^+1.
文摘An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.
基金supported by JSPS Grant-in-Aid for Scientific Research(B)(Grant No.16H03937)Challenging Exploratory Research+1 种基金supported by National Natural Science Foundation of China(Grant No.11771154)by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2018)。
文摘In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spacesℝn^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spacesℝn^+1.
