Promotion and cyclic sieving on families of SSYT

We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as CSP-polynomial. The second family we consider consists of skew shapes, consisting of rectangles. Again, the charge generating polynomial together with promotion exhibits the cyclic sieving phenomenon. This generalizes earlier result by B. Rhoades and later B. Fontaine and J. Kamnitzer. Finally, we consider certain skew ribbons, where promotion behaves in a predictable manner. This result is stated in form of a bicyclic sieving phenomenon. One of the tools we use is a novel method for computing charge of skew semistandard tableaux, in the case when every number in the tableau occur with the same frequency

Refined Catalan and Narayana cyclic sieving

We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of "ears", non-crossing matchings with a fixed number of short edges, and non-crossing configurations with a fixed number of loops and edges.Comment: Updated version, minor change

К вопросу о параметрической оптимизации механизма очистки зерноуборочного комбайна

We investigated by electron spectroscopy the strong-field multiphoton ionization of O-2 molecules with ultrashort laser pulses in the intensity range between the multiphoton and tunneling regimes. The ionization proceeds by at least three different mechanisms, in addition to the eight- and nine-photon nonresonant pathways. Transient multiphoton resonances with vibrational Rydberg levels give rise to direct Freeman-type peaks with sublaser linewidth and spin-orbit splitting. Some resonance levels actually become populated and yield extremely narrow lines because of postpulse vibrational autoionization. When the lowest photon order resonance channel for the Rydberg states is closed, a third contribution becomes dominant with a main peak at 0.4 eV that shares its main properties with the recently discovered universal low-energy structure in the electron spectra of atoms and molecules [C. I. Blaga et al., Nat. Phys. 5, 335 (2009); W. Quan et al., Phys. Rev. Lett. 103, 093001 (2009)]. The variation of the Freeman resonance spectrum with the laser peak intensity is well correlated with the vibronic Franck-Condon factors for the overlap of the intermediate Rydberg state with the O-2 ground state. Accordingly, the Freeman peaks could be unambiguously assigned to individual vibronic multiphoton resonances, and the disappearance of the Freeman resonances at a certain laser intensity could be explained. The population of the autoionizing Rydberg states could be assigned similarly to such vibronic resonances

Single-photon multiple ionization processes studied by electron coincidence spectroscopy

This thesis is based on studies of multiple ionization of atoms and molecules induced by the absorption of a single photon. For the experimental investigations a time-of-flight magnetic bottle spectrometer has been used to detect the emitted electrons in coincidence. The method of coincidence time-of-flight spectroscopy and the experimental setup used is described. Experimental and theoretical results on molecular double core holes (DCHs) and multiple ionization of atoms are presented. Molecular DCHs are of considerable interest, as their chemical shifts are predicted to be more sensitive than their single core hole counterparts. Using CH4 and NH3 as examples, it is shown that molecules with two vacancies in the innermost shell can be studied using synchrotron light in combination with our coincidence technique. The chemical shifts of S 2p DCHs are investigated for the molecules CS2, H2S and SO2 and the influence of relaxation effects on the shifts are estimated. In the studies of atoms, the main focus is on the processes leading to double and higher degrees of ionization, and the final state populations. In cadmium double photoionization in the photon energy region 40-200 eV occurs mainly by indirect ionization via valence ionized satellite states and through Coster-Kronig decay of inner shell hole states. In valence-valence ionization of krypton by 88 eV photons both direct and indirect ionization processes are found to be important. For the indirect pathways strong final state selectivity in the autoionization decays of the intermediate states is observed. Triple ionization of krypton via intermediate core-valence doubly ionized states is investigated. The intermediate states are observed in the energy region 120-125 eV, and their decay to states of the triply charged ion is mapped. Experimental and theoretical results on the formation of 2p double hole states in argon are presented.At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.</p

Refined Catalan and Narayana cyclic sieving

We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type $A$ and type $B$. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of "ears", non-crossing matchings with a fixed number of short edges, and non-crossing configurations with a fixed number of loops and edges.Keywords: Dyck paths, cyclic sieving, Narayana numbers, major index, q-analog.Mathematics Subject Classifications: 05E18, 05A19, 05A3

Refined Catalan and Narayana cyclic sieving

We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of “ears”, non-crossing matchings with a fixed number of short edges, and non-crossing configurations with a fixed number of loops and edges