Preprint Series
This page is an electronic archive of the preprints of Statistics & Mathematics Unit, Indian Statistical Institute, Bangalore Centre.

Preprints (2015)

  • Anil Kumar C P and Sunil Prajapati
    Maximal Non-commuting Sets in Unipotent Upper-triangular Linear Group $UU_4(\mathbb{F}_q)$
    [Full article pdf]
    Abstract: We find out the exact size of the maximal non-commuting sets in unipotent upper triangular matrix group $UU_4(\mathbb{F}_q)$ in terms of a non-commuting geometric structure. Then we get bounds on the size of this set by explicitly finding certain non-commuting sets in the geometric configuration.
    February 18, 2015
    isibc/ms/2015/1
  • Gugan Thoppe, D. Yogeshwaran and Robert J. Adler
    On the evolution of topology in dynamic Erdös-Rényi graphs.
    [Full article pdf]
    Abstract: We study a time varying analogue of the \ER graph, which we call the dynamic \ER graph, and concentrate on the topological aspects of its clique complex. Denoting the graph on $n$ points, with edge connection probability $p$, and at time $t$, by $G(n, p, t)$, the dynamics is determined by each edge of the graph independently evolving as a on/off Markov chain. Our main result is that if $p = n^\alpha$, with $\alpha \in (-1/k, -1/(k + 1))$, then the time dynamics of the normalized $k-$th Betti number of the clique complex associated with the graph converges in distribution to that of the stationary Ornstein-Uhlenbeck process as $n \rightarrow \infty$.
    April 3, 2015
    isibc/ms/2015/2
  • Prateep Chakraborty and Shreedevi K. Masuti
    Maps between $G_{n,k}$ and $G_{n,l}$
    [Full article pdf]
    Abstract: Let $G_{n,k}$ denote the Grassmann manifold of $k$-dimensional vector subspaces of $\mathbb{C}^n$ and $[X,Y]$ denote the set of homotopy classes of maps from $X$ to $Y$. We show that (1) $[G_{n,l},G_{n,k}]$ is finite if $k < l$ and $n\geq 2l^2+l-2,$ (2) $[G_{n,k},G_{n,l}]$ is finite if $2< k< l<2(k-1)$ and $n\geq 3l^2-2,$ (3) $[G_{n,k},G_{n,l}]$ is finite if $1< k< l$, $f> f_1$ and $n\geq 3l^2-2$, where $l=ek+f$ and $n=e_1k+f_1$ with $0\leq f,f_1< k.$ In all these cases each homotopy class is rationally null-homotopic.
    May 13, 2015
    isibc/ms/2015/3
  • Prateep Chakraborty and Ajay Singh Thakur
    Nonexistence of Almost Complex Structures on the product $S^{2m} \times M$
    [Full article pdf] [Arxiv link]
    Abstract: In this note we give a necessary condition for having an almost complex structure on the product $S^{2m} \times M$, where $M$ is a connected orientable closed manifold. We show that if the Euler characteristic $\chi(M) \neq 0$, then except for finitely many values of $m$, we do not have almost complex structure on $S^{2m} \times M$. In the particular case when $M = \mathbb C \mathbb P^n, n \neq 1$, we show that if $n \not \equiv 3 \pmod 4$ then $S^{2m} \times \mathbb C \mathbb P^{n}$ has an almost complex structure if and only if $m = 1,3$. As an application we obtain conditions on the nonexistence of almost complex structure on Dold manifolds.
    Aug 26, 2015
    isibc/ms/2015/4
    • Preprints (2014) Preprints (2013) Preprints (2012) Preprints (2012) Preprints (2011) Preprints (2010) Preprints (2009) Preprints (2008) Preprints (2007) Preprints (2006) Preprints (2005)
    Preprint Series: Delhi Centre; Kolkata Centre.
     | This page last modified on: October 20th, 2014  | Statmath Unit |  ISI Bangalore Centre |  ISI Delhi Centre |  ISI Kolkata Centre |