Academic Journal
Constructing generalized Heffter arrays via near alternating sign matrices
| العنوان: | Constructing generalized Heffter arrays via near alternating sign matrices |
|---|---|
| المؤلفون: | Mella L., Traetta T. |
| المساهمون: | Mella L., Traetta T. |
| سنة النشر: | 2024 |
| المجموعة: | Università degli Studi di Brescia: OPENBS - Open Archive UniBS |
| مصطلحات موضوعية: | Biembedding, Generalized Heffter array, Near alternating sign matrice, Orthogonal decomposition, Simple sequences |
| الوصف: | Let S be a subset of a group G (not necessarily abelian) such that S∩−S is empty or contains only elements of order 2, and let h=(h1,.,hm)∈Nm and k=(k1,.,kn)∈Nn. A generalized Heffter array GHASλ(m,n;h,k) over G is an m×n matrix A=(aij) such that: the i-th row (resp. j-th column) of A contains exactly hi (resp. kj) nonzero elements, and the list {aij,−aij|aij≠0} equals λ times the set S∪−S. We speak of a zero sum (resp. nonzero sum) GHA if each row and each column of A sums to zero (resp. a nonzero element), with respect to some ordering. In this paper, we use near alternating sign matrices to build both zero and nonzero sum GHAs, over cyclic groups, having the further strong property of being simple. In particular, we construct zero sum and simple GHAs whose row and column weights are congruent to 0 modulo 4. This result also provides the first infinite family of simple (classic) Heffter arrays to be rectangular (m≠n) and with less than n nonzero entries in each row. Furthermore, we build nonzero sum GHASλ(m,n;h,k) over an arbitrary group G whenever S contains enough noninvolutions, thus extending previous nonconstructive results where ±S=G∖H for some subgroup H of G. Finally, we describe how GHAs can be used to build orthogonal decompositions and biembeddings of Cayley graphs (over groups not necessarily abelian) onto orientable surfaces. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | STAMPA |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/wos/WOS:001202817800001; volume:205; numberofpages:26; journal:JOURNAL OF COMBINATORIAL THEORY. SERIES A; https://hdl.handle.net/11379/593485 |
| DOI: | 10.1016/j.jcta.2024.105873 |
| الاتاحة: | https://hdl.handle.net/11379/593485 https://doi.org/10.1016/j.jcta.2024.105873 |
| Rights: | info:eu-repo/semantics/embargoedAccess |
| رقم الانضمام: | edsbas.90128A56 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.jcta.2024.105873 |
|---|