Lozenge tilings with free boundaries

We study lozenge tilings of a domain with partially free boundary. In particular, we consider a trapezoidal domain (half hexagon), s.t. the horizontal lozenges on the long side can intersect it anywhere to protrude halfway across. We show that the positions of the horizontal lozenges near the opposite flat vertical boundary have the same joint distribution as the eigenvalues from a Gaussian Unitary Ensemble (the GUE-corners/minors process). We also prove the existence of a limit shape of the height function, which is also a vertically symmetric plane partition. Both behaviors are shown to coincide with those of the corresponding doubled fixed-boundary hexagonal domain. We also consider domains where the different sides converge to $\infty$ at different rates and recover again the GUE-corners process near the boundary.Comment: 27 pages, 4 figures; version 2-- typos fixed, improved proofs and computations, incorporated referee's comments. To appear in Letters in Mathematical Physic

Tableaux and plane partitions of truncated shapes

We consider a new kind of straight and shifted plane partitions/Young tableaux --- ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted staircase without the box in its upper right corner, i.e. truncated by a box, a rectangle truncated by a staircase and a rectangle truncated by a square minus a box. The proofs involve finding the generating function of the corresponding plane partitions using interpretations and formulas for sums of restricted Schur functions and their specializations. The number of standard tableaux is then found as a certain limit of this function.Comment: Accepted to Advances in Applied Mathematics. Final versio

Monastic Traditions and Practices in Macedonia and Their Implications in Modern Times

The purpose of this paper is to present several fundamental aspects in the reconstruction of the issue related to the monasticism in Macedonia. In that sense, taken into consideration is the historical and spiritual continuity of the monasticism beginning from the ninth century to modern times, as well as the monastic practices established in the existing typicons, and the implications of the revival of the modern monasticism in Macedonia in the 1990s. Research at digressive methodological level points to the fact that in monasticism, the same traditional Christian values are cherished as they have been cherished in the previous period. Namely, monasticism does not represent only a spiritual accomplishment and enthusiasm, but also a movement consisting of cultural-educational, artistic and philanthropic tendencies

Medieval Heresis and Protestantism

In addition to the current social and political circumstances, the appearance of heresies and reform movements during the Middle Ages. was largely determined by the educational tendencies and movement of humanism, which concentrated on the matter of the human being. Thisarticle offers a digressive analysis that examines the appearance, essence, and significance of Bogomilism, Catharism, Waldensians and their implications for later reform movements—more specifically Protestantism. It should be emphasized that in this context, such ideas, characteristic of medieval heresies, impacted Protestantism, as seen in the works of John Wycliffe (1328-1384) and Jan Hus (1369-1415). In fact, they were qualified to be Protestants even before the appearance of Protestantism as a movement, and Martin Luther (1483-1546), the bearer of the Reformation for his time, was well-informed of their works. Luther was also familiar with the movement of the Waldensians, which certainly had its own impact on the further development and establishment of Protestantism, even though it followed a period of mutual cooperation between the two communities

Confirmatory News

This paper investigates how competition in the media affects the quality of news. In our model, demand for news depends on the market perception of the media's ability to receive correct information: it is positive if and only if news is potentially useful for the voting decision. When the media receives information which contradics commonly shared priors, it either reports this information or it confirms the priors: "most likely, my information is correct, but my potential buyers may be unable to assess the quality of news and attribute it according to common priors". We ask whether competition may help to elicit information from the media. Our answer is positive when news covers issues on which the priors are sufficiently precise, or the follow-up quality assessment is a likely event. However, when news concerns controversial issues and it is hardly possible to asses its quality, competitive pressures induce confirmatory reporting.Competition in the media, quality of news, common priors, reputational cheap-talk

Campaign Promises and Political Factions

This paper builds a dynamic model of electoral competition with nonbinding campaign promises. We find that campaign promises by a candidate for office signal her political preferences and public policy that she intends to implement. The reason is that electoral competition induces her to pander campaign promises to political interests by a minimal majority of citizens. If their votes bring her in office, she has to raise them once again in order to be re-elected. For that, she needs to fulfill her electoral promises. To minimize the cost of pandering to re-election if in office, a candidate gives campaign promises that she would like to fulfill the most. She fulfills them if in office, unless the cost of fulfillment lies above the benefit from re-election. We show, furthermore, that representatives by a minimal majority of citizens form a faction to coordinate their electoral strategies, and we investigate the consequences of such political collusion.Electoral promises, pork-barrel politics, political parties

On the complexity of computing Kronecker coefficients

We study the complexity of computing Kronecker coefficients $g(\lambda,\mu,\nu)$. We give explicit bounds in terms of the number of parts $\ell$ in the partitions, their largest part size $N$ and the smallest second part $M$ of the three partitions. When $M = O(1)$, i.e. one of the partitions is hook-like, the bounds are linear in $\log N$, but depend exponentially on $\ell$. Moreover, similar bounds hold even when $M=e^{O(\ell)}$. By a separate argument, we show that the positivity of Kronecker coefficients can be decided in $O(\log N)$ time for a bounded number $\ell$ of parts and without restriction on $M$. Related problems of computing Kronecker coefficients when one partition is a hook, and computing characters of $S_n$ are also considered.Comment: v3: incorporated referee's comments; accepted to Computational Complexit

Congruence Among Voters and Contributions to Political Campaigns

This paper builds a theory of electoral campaign contributions. Interest groups contribute to political campaigns to signal their private information on the valence of candidates for office. Campaign contributions by an interest group enhance electoral fortunes by a candidate who is valent with this group. The candidate preferred by an interest group whose private information is the most precise receives the highest contributions and wins political office. Campaign contributions are smaller than donor electoral sorting benefits.Campaign contributions, incumbency advantage