20.500.12556/RUL-180858 Generalized rank functions and quilts of alternating sign matrices In this paper, we present new objects, quilts of alternating sign matrices with respect to two given posets. Quilts generalize several commonly used concepts in mathematics. For example, the rank function on submatrices of a matrix gives rise to a quilt with respect to two Boolean lattices. When the two posets are chains, a quilt is equivalent to an alternating sign matrix and its corresponding corner sum matrix. Quilts also generalize the monotone Boolean functions counted by the Dedekind numbers. Quilts form a distributive lattice with many beautiful properties and contain many classical and well-known sublattices, such as the lattice of matroids of a given rank and ground set. While enumerating quilts is hard in general, we prove two major enumerative results, when one of the posets is an antichain and when one of them is a chain. We also give some bounds for the number of quilts when one poset is the Boolean lattice. quilts alternating sign matrices Dedekind numbers distributive lattice true false true Angleški jezik Angleški jezik Članek v reviji 2026-03-18 10:53:20 2026-03-18 10:53:20 2026-03-21 03:55:12 0000-00-00 00:00:00 2026 0 0 45 str. article no. 110863 Vol. 491 May 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-05-01 519.1 0001-8708 10.1016/j.aim.2026.110863 272054531 1-s2.0-S000187082600085X-main.pdf 1-s2.0-S000187082600085X-main.pdf 1 AC33D9835BE36459E0CF19FD1B34A17E e2c5a106bab1b4786b3c11d271744687e280fba77850d8f10c899062b3a675b7 9848038b-22b0-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=230768 https://www.sciencedirect.com/science/article/pii/S000187082600085X 1 390f9c85-22b0-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=230767 Fakulteta za matematiko in fiziko 0 0 0