?ュ??瀛﹁??锛?Tommaso Traetta ??????

?ュ??????浣?锛?University of Brescia, Italy 

?ュ???堕?达?2024骞???18?ワ??ㄥ??锛?涓???4:30-5:30

?ュ???扮?癸? 瀛︾??娲诲?ㄤ腑蹇?10灞?浼?璁??  

?ュ????瑕?锛?A near alternating sign matrix (NASM) is an $m\times n$ array with entries from $\{0, \pm1\}$ such that, ignoring $0$s, the $+1$s and $-1$s alternate in each row and each column; in addition, we require such a matrix to have arbitrarily prescribed weights for each row and column. These arrays, which generalize alternating sign matrices, were studied for the first time by Brualdi and Kim [2], although they focused on constructing them, leaving out the weights, but with arbitrarily prescribed first and last nonzero entries in each row and column. It is well known that these matrices have connections with partitions, tilings, and statistical physics. 

Another class of combinatorial arrays, known as Heffter arrays, was introduced by Archdeacon in 2015 [1] as a tool to construct current graphs, orthogonal cycle systems and biembeddings of complete graphs. 

In this talk, we will describe some constructive methods [4] and show an application of NASMs to build (generalized) Heffter arrays [3] satisfying further properties that allow us to obtain orthogonal cycle systems and biembeddings of Cayley graphs.