Letn andk be arbitrary positive integers,p a prime number and L(k n)(p) the subgroup lattice of the Abelianp-group (Z/p k ) n . Then there is a positive integerN(n,k) such that whenp N(n,k),L (k N )(p) has the strong ...Letn andk be arbitrary positive integers,p a prime number and L(k n)(p) the subgroup lattice of the Abelianp-group (Z/p k ) n . Then there is a positive integerN(n,k) such that whenp N(n,k),L (k N )(p) has the strong Sperner property.展开更多
Let V n(q) be the n dimensional vector space over the finite field with q elements, K a k dimensional subspace and C the set of the subspaces S such that S∩K≠=O .We show that C ...Let V n(q) be the n dimensional vector space over the finite field with q elements, K a k dimensional subspace and C the set of the subspaces S such that S∩K≠=O .We show that C is Sperner and unimodal and point out all maximum sized antichains in C .For the Whitney number W m of C , we show that W m 2 qW m 1 W m+1 has nonnegative coefficients as a polynomial in q and that W 0W nW 1W n 1 W 2… .展开更多
文摘Letn andk be arbitrary positive integers,p a prime number and L(k n)(p) the subgroup lattice of the Abelianp-group (Z/p k ) n . Then there is a positive integerN(n,k) such that whenp N(n,k),L (k N )(p) has the strong Sperner property.
文摘Let V n(q) be the n dimensional vector space over the finite field with q elements, K a k dimensional subspace and C the set of the subspaces S such that S∩K≠=O .We show that C is Sperner and unimodal and point out all maximum sized antichains in C .For the Whitney number W m of C , we show that W m 2 qW m 1 W m+1 has nonnegative coefficients as a polynomial in q and that W 0W nW 1W n 1 W 2… .
