Brunn-Minkowski Inequalities for Contingency Tables and Integer Flows
| dc.creator | Barvinok, Alexander | |
| dc.date | 2006-03-28 | |
| dc.date.accessioned | 2026-07-07T07:07:17Z | |
| dc.date.available | 2026-07-07T07:07:17Z | |
| dc.description | Given a non-negative mxn matrix W=(w_ij) and positive integer vectors R=(r_1, >..., r_m) and C=(c_1, ..., c_n), we consider the total weight T(R, C; W) of mxn non-negative integer matrices (contingency tables) D with the row sums r_i, the column sums c_j, and the weight of D=(d_ij) equal to product of w_ij^d_ij. In particular, if W is a 0-1 matrix, T(R, C; W) is the number of integer feasible flows in a bipartite network. We prove a version of the Brunn-Minkowski inequality relating the numbers T(R, C; W) and T(R_k, C_k; W), where (R, C) is a convex combination of (R_k, C_k) for k=1, ..., p. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603655 | |
| dc.identifier | http://arxiv.org/abs/math/0603655 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110337 | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 05A16, 52B12, 52B20, 52A41 | |
| dc.title | Brunn-Minkowski Inequalities for Contingency Tables and Integer Flows | |
| dc.type | text |