A Bijective Proof of an Unbalanced Wilf Equivalence
We find a bijection to prove that the set of patterns {3412, 4321} is Wilf-equivalent to the set of patterns {3412, 4231, 45321, 54312}.
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arXiv subjects
Michael Waite
Publications and source records attributed to Michael Waite.
Permutations with a fixed number of occurrences of a pattern: A case generalizing 231
We determine a set of permutation patterns $q$ so that the number of permutations with $r$ occurrences of $q$ is asymptotically $n^r$ times the number of permutations avoiding $q$, partially settling a conjecture of Conway and Guttman. We also use these asymptotics to prove nonrationality and nonalgebraicity for certain ordinary generating functions for permutations with $r$ copies of a pattern.
math.CO↗
Permutations with a fixed number of occurrences of a monotone pattern
We bound the number of permutations with a fixed number $r$ of $321 \ominus p_0$ patterns by a constant times the number of permutations which avoid $321 \ominus p_0$. We use this new upper bound to show that the ordinary generating function for permutations with $r$ copies of $k(k-1)...1$ is not rational for odd $k \geq 3$ and not algebraic for even $k \geq 3$.
math.CO↗
Assessing trade-offs among electrification and grid decarbonization in a clean energy transition: Application to New York State
A modeling framework is presented to investigate trade-offs among decarbonization from increased low-carbon electricity generation and electrification of heating and vehicles. The model is broadly applicable but relies on high-fidelity parameterization of existing infrastructure and anticipated electrified loads; this study applies it to New York State where detailed data is available. Trade-offs are investigated between end use electrification and renewable energy deployment in terms of supply costs, generation and storage capacities, renewable resource mix, and system operation. Results indicate that equivalent emissions reductions can be achieved at lower costs to the grid by prioritizing electrification with 40-70% low-carbon electricity supply instead of aiming for complete grid decarbonization. With 60% electrification and 50% low-carbon electricity, approximately 1/3 emissions reductions can be achieved at current supply costs; with only 20% electrification, 90% low-carbon electricity is required to achieve the same emissions reductions, resulting in 43% higher grid costs. In addition, three primary cost drivers are identified for a system undergoing decarbonization: (1) decreasing per-unit costs of existing infrastructure with increasing electrified demand, (2) higher in-state generation costs from low-carbon sources relative to gas-based and hydropower generation, and (3) increasing integration costs at high percentages of low-carbon electricity.
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