Face numbers of triangulations of simplicial complexes were studied by Stanley by use of his concept of a local h-vector. It is shown that a parallel theory exists for cubical subdivisions of cubical complexes, in which the role of the h-vector of a simplicial complex is played by the (short or long) cubical h-vector of a cubical complex, defined by Adin, and the role of the local h-vector of a...

The semi-enclosed bays impacted by heavy anthropogenic activities have weak water exchange and purification capacities. Most of the sea suffered severe eutrophication, quality deterioration, ecosystem degradation other problems. Although many countries local governments carried out corresponding environmental protection actions, evaluation their effectiveness still requires monitoring technolog...

The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 2 th Catalan number otherwise. We present an involution that proves a refinement of this sign-balance property respecting the length of the longest increasing subsequence of the permutation. In addition, this yields a combinatorial proof of a recent analogous resul...

A decisão do STF na ADIN n. 5.766 declarou inconstitucionais os arts. 790-B, caput e § 4º, 791-A, da Consolidação das Leis Trabalho (CLT) não trouxe qualquer limite temporal à sua aplicação. São dois argumentos principais para continuidade cobrança dos honorários periciais beneficiários justiça gratuita, mesmo depois publicação de referida decisão: 1) o acórdão julgamento ainda foi publicado; 2...

In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the generating function of the fmajk indices of colored permutations. The second result is a combinatorial treatment of a relation on the q-derangement numbers ...

A notion of cyclic descents on standard Young tableaux (SYT) rectangular shape was introduced by Rhoades, and extended to certain skew shapes Adin, Elizalde Roichman. The descent set restricts the usual when largest value is ignored, has property that number SYT a given with D invariant under shifts entries D. Reiner Roichman proved map if only it not connected ribbon. Unfortunately, their proo...