Some bounds for relative autocommutativity degree

Some Lower Bounds for Estrada Index

Betti Numbers and Degree Bounds for Some Linked Zero-schemes

In [8], Herzog and Srinivasan study the relationship between the graded Betti numbers of a homogeneous ideal I in a polynomial ring R and the degree of I. For certain classes of ideals, they prove a bound on the degree in terms of the largest and smallest Betti numbers, generalizing results of Huneke and Miller in [9]. The bound is conjectured to hold in general; we study this using linkage. If...

Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

Lower Degree Bounds for

We prove two statements. The rst one is a conjecture of Ian Hughes which states that if f1; : : : ; fn are primary invariants of a nite linear group G, then the least common multiple of the degrees of the fi is a multiple of the exponent of G. The second statement is about vector invariants: If G is a permutation group and K a eld of positive characteristic p such that p divides jGj, then the i...

Some bounds for the relative generalized Hamming weights of some evaluation codes

In this paper we find some bounds for the relative generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. Also we compare the relative generalized Hamming weights of the codes CX(d) and CX′(d) when X ′ is embedded in X. We use these results to obtain some lower bounds for the relative generalized Hamming weights of the codes parameterized by the edges ...