SEPTEM VERBA A CHRISTO W STAROPOLSKICH APOKRYFACH NOWOTESTAMENTALNYCH W PERSPEKTYWIE ŹRÓDŁOZNAWCZEJ I LINGWISTYCZNEJ. CZĘŚĆ DRUGA: JĘZYKOWE UKSZTAŁTOWANIE

This article is the second and the last part of a series dedicated to the characteristics of a description of Christ’s seven words uttered on the cross as accounted in Old Polish biblical and apocryphal narrations. In part one, I focus on the origin of the words, the characteristics of Old Polish texts containing them. I highlight the most important differences in the narration of the specific fragments of Old Polish Passions of Jesus. Part two is entirely dedicated to the language of the fragments of Old Polish texts on Christ’s seven words uttered on the cross (ŻPJK, SCh and RD). First, I present the enumeration schemes in each apocrypha. They are strictly related to the tradition of religious instruction and teaching and are an attempt at sorting out the material. The article presents also the various ways in which Christ’s specific words are called. The regular word-forming structure of the modifiers affects the rhythmic form of the specific fragments of texts. Finally, I show how quotations from Christ were introduced into each apocrypha: how the utterances’ modal frame was shaped and what verbs of speech were used. It turns out that in each historic text, Christ’s words were treated differently: in the SCh, they were described most extensively and in the RD – least extensively but it is the RD where the enumerations are most precise with respect to the syntax, perhaps because the specific parts are at the smallest distance from each other. Christ’s seven words on the cross are least structured in the ŻPJK.

Refining Enumeration Schemes to Count According to Permutation Statistics

We develop algorithmic tools to compute quickly the distribution of permutation statistics over sets of pattern-avoiding permutations. More specfically, the algorithms are based on enumeration schemes, the permutation statistics are based on the number of occurrences of certain vincular patterns, and the permutations avoid sets of vincular patterns. We prove that whenever a finite enumeration scheme exists to count the number of pattern-avoiding permutations, then the distribution of statistics like the number of descents can also be computed based on the same scheme. Statistics such as the number of peaks, right-to-left maxima, and the major index are also investigated, as well as multi-statistics.

Influence of enumeration time periods on detecting community parameters of periphytic diatoms using an artificial substratum in coastal waters

Community parameters of diatoms have been used as useful bioindicators for bioassessment of both lentic and lotic systems. The influence of enumeration time periods on detecting community parameters of periphytic diatom assemblages within different exposure times was studied using an artificial substratum in coastal waters of the Yellow Sea, northern China, during the period May–June 2010. Samples were collected at a depth of 1 m, and were examined with different enumeration time periods. Enumeration time periods represented a significant influence on detecting the community features of periphytic diatoms, although no significant changes occurred in periphytic diatom community structure between two enumeration schemes (within 24 h and 24–48 h). The delayed enumeration (within 24–48 h) may result in the similarity of the communities being reduced 10–29%, and in species numbers decreasing and in abundance increasing with exposure duration, respectively. The diversity (richness, evenness and diversity of species) indices were significantly decreased in almost all samples with >10% standard errors at some exposure times by the delayed enumeration scheme. These results suggest that the delayed enumeration may have resulted in the species richness and individual abundance of periphytic diatoms significantly decreasing and increasing, respectively, and thus significantly affected the analyses of species diversity for assessing water quality in marine ecosystems.

Enumeration Schemes for Permutations Avoiding Barred Patterns

We give the first comprehensive collection of enumeration results for permutations that avoid barred patterns of length $\leq 4$. We then use the method of prefix enumeration schemes to find recurrences counting permutations that avoid a barred pattern of length $>4$ or a set of barred patterns.

Enumeration Schemes for Restricted Permutations

Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple packageWilfPlus, which implements this process. We also compare enumeration schemes to three other systematic enumeration techniques: generating trees, substitution decompositions, and the insertion encoding.