A simple note on the Yoneda (co)algebra of a monomial algebra

E. Herscovich

doi:10.37863/umzh.v73i2.6040

A simple note on the Yoneda (co)algebra of a monomial algebra

Ukrains’kyi Matematychnyi Zhurnal ◽

10.37863/umzh.v73i2.6040 ◽

2021 ◽

Vol 73 (2) ◽

pp. 275-277

Author(s):

E. Herscovich

Keyword(s):

Linear Combination ◽

Short Note ◽

Simple Argument ◽

Monomial Algebra

UDC 512.7 If is a monomial -algebra, it is well-known that is isomorphic to the space of (Anick) -chains for . The goal of this short note is to show that the next result follows directly from well-established theorems on -algebras, without computations: there is an -coalgebra model on satisfying that, for and , is a linear combination of , where , and . The proof follows essentially from noticing that the Merkulov procedure is compatible with an extra grading over a suitable category. By a simple argument based on a result by Keller we immediately deduce that some of these coefficients are .

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A SHORT NOTE ON THE FRAME SET OF ODD FUNCTIONS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972718000746 ◽

2018 ◽

Vol 98 (3) ◽

pp. 481-493 ◽

Cited By ~ 4

Author(s):

MARKUS FAULHUBER

Keyword(s):

Wigner Distribution ◽

Short Note ◽

Gabor Frame ◽

Gabor Frames ◽

Simple Argument ◽

Gabor Systems ◽

One Dimensional ◽

Separable Case ◽

The One ◽

Frame Set

We give a simple argument which shows that Gabor systems consisting of odd functions of$d$variables and symplectic lattices of density$2^{d}$cannot constitute a Gabor frame. In the one-dimensional, separable case, this follows from a more general result of Lyubarskii and Nes [‘Gabor frames with rational density’,Appl. Comput. Harmon. Anal.34(3) (2013), 488–494]. We use a different approach exploiting the algebraic relation between the ambiguity function and the Wigner distribution as well as their relation given by the (symplectic) Fourier transform. Also, we do not need the assumption that the lattice is separable and, hence, new restrictions are added to the full frame set of odd functions.

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On the Stanley-Wilf Conjecture for the Number of Permutations Avoiding a Given Pattern

The Electronic Journal of Combinatorics ◽

10.37236/1477 ◽

1999 ◽

Vol 6 (1) ◽

Cited By ~ 34

Author(s):

Richard Arratia

Keyword(s):

Recent Work ◽

Short Note ◽

Random Permutations ◽

Simple Argument ◽

Sigma 1 ◽

Wilf Conjecture

Consider, for a permutation $\sigma \in {\cal S}_k$, the number $F(n,\sigma)$ of permutations in ${\cal S}_n$ which avoid $\sigma$ as a subpattern. The conjecture of Stanley and Wilf is that for every $\sigma$ there is a constant $c(\sigma) < \infty$ such that for all $n$, $F(n,\sigma) \leq c(\sigma)^n$. All the recent work on this problem also mentions the "stronger conjecture" that for every $\sigma$, the limit of $F(n,\sigma)^{1/n}$ exists and is finite. In this short note we prove that the two versions of the conjecture are equivalent, with a simple argument involving subadditivity We also discuss $n$-permutations, containing all $\sigma \in {\cal S}_k$ as subpatterns. We prove that this can be achieved with $n=k^2$, we conjecture that asymptotically $n \sim (k/e)^2$ is the best achievable, and we present Noga Alon's conjecture that $n \sim (k/2)^2$ is the threshold for random permutations.

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Introduction

10.3366/edinburgh/9781474427234.003.0001 ◽

2018 ◽

Cited By ~ 1

Author(s):

Peter Hopkins

Keyword(s):

Final Section ◽

Short Note ◽

Current Situation ◽

Research Projects ◽

Everyday Lives ◽

Early Settlement ◽

The Everyday ◽

Initial Research

The chapters in this collection explore the everyday lives, experiences, practices and attitudes of Muslims in Scotland. In order to set the context for these chapters, in this introduction I explore the early settlement of Muslims in Scotland and discuss some of the initial research projects that charted the settlement of Asians and Pakistanis in Scotland’s main cities. I then discuss the current situation for Muslims in Scotland through data from the 2011 Scottish Census. Following a short note about the significance of the Scottish context, in the final section, the main themes and issues that have been explored in research about Muslims in Scotland.

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Short Note: A Record of Twin Fetuses in a Harbor Porpoise (Phocoena phocoena) Stranded on the Dutch Coast

Aquatic Mammals ◽

10.1578/am.40.4.2014.394 ◽

2014 ◽

Vol 40 (4) ◽

pp. 394-397 ◽

Cited By ~ 1

Author(s):

Lonneke L. IJsseldijk ◽

Andrea Gröne ◽

Sjoukje Hiemstra ◽

Jeroen Hoekendijk ◽

Lineke Begeman

Keyword(s):

Short Note ◽

Phocoena Phocoena ◽

Harbor Porpoise ◽

Dutch Coast

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Short Note: Habitat Characteristics of the Critically Endangered Taiwanese Humpback Dolphins (Sousa chinensis) of the Eastern Taiwan Strait

Aquatic Mammals ◽

10.1578/am.40.4.2014.368 ◽

2014 ◽

Vol 40 (4) ◽

pp. 368-374 ◽

Cited By ~ 7

Author(s):

Lauren E. Dares ◽

Jordan M. Hoffman ◽

Shih Chu Yang ◽

John Y. Wang

Keyword(s):

Short Note ◽

Taiwan Strait ◽

Habitat Characteristics ◽

Critically Endangered ◽

Sousa Chinensis

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Short Note: Predation of Harbour Porpoises (Phocoena phocoena) by Grey Seals (Halichoerus grypus) in Wales

Aquatic Mammals ◽

10.1578/am.41.2.2015.188 ◽

2015 ◽

Vol 41 (2) ◽

pp. 188-191 ◽

Cited By ~ 10

Author(s):

Thomas Stringell ◽

Dave Hill ◽

Dafydd Rees ◽

Ffion Rees ◽

Padrig Rees ◽

...

Keyword(s):

Short Note ◽

Halichoerus Grypus ◽

Phocoena Phocoena

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Impact of Optimal Cropping Patterns on Incomes in a Punjab District

The Pakistan Development Review ◽

10.30541/v15i2pp.218-221 ◽

1976 ◽

Vol 15 (2) ◽

pp. 218-221

Author(s):

M. Arshad Chaudhry

Keyword(s):

Developing Countries ◽

Linear Programming ◽

Short Note ◽

Cropping Pattern ◽

Small Farms ◽

Cropping Patterns ◽

Punjab Province ◽

Optimal Cropping

To improve farm incomes in developing countries, the foremost question that the farmer must address himself to is: what cropping pattern best uses the fixed resources in order to get the highest returns? During the last decade, the agricultural economists have shown great interest in applying the tools of linear programming to individual farms. Most of the studies conducted elsewhere have shown that, under existing cropping pattern, farm resources were not being utilized optimally on the small farms.[l, 4]. We conducted a survey in the canal-irrigated areas of the Punjab province of Pakistan1 to investigate into the same problem. This short note aims at identifying the opti¬mal cropping pattern and to estimate the increase in farm incomes as a result of a switch towards it on the sampled farms.

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