Generalized rank functions and quilts of alternating sign matrices

Billey, Sara C. (avtor), Konvalinka, Matjaž (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: quilts, alternating sign matrices, Dedekind numbers, distributive lattice
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.05.2026
• Leto izida: 2026
• Št. strani: 45 str.
• Številčenje: Vol. 491, article no. 110863
• PID: 20.500.12556/RUL-180858
• UDK: 519.1
• ISSN pri članku: 0001-8708
• DOI: 10.1016/j.aim.2026.110863
• COBISS.SI-ID: 272054531
• Datum objave v RUL: 18.03.2026

Gradivo je del revije

• Naslov: Advances in mathematics
• Skrajšan naslov: Adv. math.
• Založnik: Elsevier
• ISSN: 0001-8708
• COBISS.SI-ID: 24891904

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.