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List of issues > Series «Mathematics». 2016. Vol. 17

The Enumeration of own t-Dimensional Subspaces of a Space Vm over the Field GF(q)

G. P. Egorychev

In the Chevalley algebra over a field K associated with any system of roots, it is allocated the niltriangular subalgebra NΦ(K) with the basis {er(r ∈ Φ+)}. In 2001 G.P. Egorychev and V.M. Levchuk had been put two problems of a enumeration of ideals: special ideals in the algebras of classical types (the problem 1) and all ideals (the problem 2). At their decision there is the problem of a finding of the number Vm,t, 1 ≤ t ≤ m, all own t-dimensional subspaces of space Vm over the field GF(q). Recently V.P. Krivokolesko and V.M. Levchuk have found an obvious expression for the number Vm,t through a multiple sum from q-combinatorial numbers. Here by means of the method of coefficients of the calculation of combinatorial sums developed by the author in the late eighties, the integral representation for numbers Vm,t is found. As consequence two simple computing formulas for these numbers were received.

a number of subspaces of space, the method of coefficients, combinatorial sums




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