Subject: Asking for referencies Date: Sat, 1 Mar 2003 17:28:34 +0100 From: "Boccellari" To: "Don Davis" Dear Professor Davies, I would like to submit to your kind attention this message. If you think it is the case, please put it in your mailing list. Recently I thought to approach the study of partition of vectors with non negative integer entries by employing algebraic topology. I don't know if this way was already examined or if it was shown to be unfruitful, with this mail I would like to ask for informations in this sense. In the following I will describe with more detail what I thought to do. Take a vector v of finite lenght n and with non-negative integer entries. An r partition of v is a family of vectors (w_1, ..., w_r) each one of finite lenght n and with non-negative integer entries such that w_1 + ... + w_r = v. A partition of v will be said non degenerate if it does't contain the null vector. A CW complex will be built which has one k cell for each k+2 non degenerate partition of v. For each non-negative integer k take the set V_k made by all k+2 partitions (w_1, ..., w_{k+2}) of v such that bot w_1 and w_{k+2} are not the null vector. Define the following degeneracies and facies operators d_i : V_k -----> V_{k-1}, and s_i : V_k -----> V_{k+1} with 0 =< i =< k as: d_i (w_1, ..., w_{k+2}) = (w_1, ..., w_i, w_{i+1} + w_{i+2}, w_{i+3}, ..., w_{k+2}) s_i (w_1, ..., w_{k+2}) = (w_1, ..., w_{i+1} , 0, w_{i+2}, ..., w_{k+2}) This defines a simplicial complex with one k cell for each k+2 non degenerate partition of v. I would like to study this complex to obtain information on the partitioning of v, in particular I am interested in the case when v is a 2n dimentional vector with all entries given by 2^n. Every help will be very welcome. Thank you for your kind attention. Yours faithfully. Tommaso Boccellari