منابع مشابه
On generalized Stanley sequences
Let N denote the set of all nonnegative integers. Let k ≥ 3 be an integer and A0 = {a1, . . . , at} (a1 < . . . < at) be a nonnegative set which does not contain an arithmetic progression of length k. We denote A = {a1, a2, . . . } defined by the following greedy algorithm: if l ≥ t and a1, . . . , al have already been defined, then al+1 is the smallest integer a > al such that {a1, . . . , al}...
متن کاملA Survey on Stanley Depth
At the MONICA conference “MONomial Ideals, Computations and Applications” at the CIEM, Castro Urdiales (Cantabria, Spain) in July 2011, I gave three lectures covering different topics of Combinatorial Commutative Algebra: (1) A survey on Stanley decompositions. (2) Generalized Hibi rings and Hibi ideals. (3) Ideals generated by two-minors with applications to Algebraic Statistics. In this artic...
متن کاملOn Characteristic Poset and Stanley Decomposition
Let J ⊂ I be two monomial ideals such that I/J is Cohen Macaulay. By associating a finite posets P g I/J to I/J , we show that if I/J is a Stanley ideal then Ĩ/J is also a Stanley ideal, where Ĩ/J is the polarization of I/J . We also give relations between sdepth and fdepth of I/J and Ĩ/J .
متن کاملOn partition functions of Andrews and Stanley
G. E. Andrews has established a refinement of the generating function for partitions π according to the numbers O(π) and O(π′) of odd parts in π and the conjugate of π, respectively. In this paper, we derive a refined generating function for partitions into at most M parts less than or equal to N , which is a finite case of Andrew’s refinement.
متن کاملOn a special class of Stanley-Reisner ideals
For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...
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ژورنال
عنوان ژورنال: THEORIA. An International Journal for Theory, History and Foundations of Science
سال: 2016
ISSN: 2171-679X,0495-4548
DOI: 10.1387/theoria.16326